MaplePrimes Questions

Hi. following on from

https://www.mapleprimes.com/questions/232817-Solving-Hanging-Cable-#comment281577

Second case: unequal poles.

I tried to work with vv's solution, but I got a problem... the required formula is

y=10.85378553130*cosh(0.0921337534371039*x) - 10.85378553130

Uneven.mw

Hi,

I have been trying to duplicate a solution to Schrodinger Eq from a utube video...the presenter use Wolfram software to graph and 

animate the plot...I have working on this all day..I a new user (several months)..any help would be appreciated.

I am attaching a screenshot

Thanks 

Frank

 

I am attaching my Maple worksheet for reference 
 

NULL

BELOW IS ADRESSING PARTICLE MOTION AND HOW ELECTRONS MOVE AROUND AND HOW MAGNETIC FIELDS AFFECTION THE MOTION OF ELECTRONS

 

PARTICLE MOTION "IGNORING SPIN" WILL COME BACK TO THAT

restart

with(Physics); interface(imaginaryunit = i)

Setup(hermitianoperators = {H, O__H, O__S}, realobjects = {`ℏ`, m, t, x_}, combinepowersofsamebase = true, mathematicalnotation = true)

[combinepowersofsamebase = true, hermitianoperators = {H, O__H, O__S}, mathematicalnotation = true, realobjects = {`ℏ`, m, t, x_}]

(1)

with(Physics[Vectors])

WAVE FUNCTION OF PARITCLE. t =time , x= some position vector

x_ = `<,>`(x, y, z)

x_ = Vector[column](%id = 36893489722226370188)

(2)

psi(t, x_)

psi(t, x_)

(3)

psi(t, x, y, z)

psi(t, x, y, z)

(4)

p_

p_

(5)

ψ is xome complex number with a real and imaginary number, the absolute value of abs(psi(t, x_))^2
`and`((is*the*probabilty*density*of*finding*the)*particle*at*postion*vector*x, at*time*t), ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, int(abs(psi(t, x_))^2, V) = 1

abs(psi(t, x_))^2

 

is*the^2*probabilty*density*of*finding*particle*at*postion*vector*x and at*time*t, ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, abs(psi(t, x_))^2*V = 1

(6)

THE ABOVE EQUATION IS TRUE IF THE WAVE FUNCTION IS "PROPERLY NORMALIZED"

THE WAVE FUNCTION EVOLVES IN TIME ACCORDING TO SCHRODINGER EQ

"`i&hbar;`(&PartialD;Psi)/(&PartialD;t)= -(`&hbar;`^(2))/(2 m)(((&PartialD;)^2)/((&PartialD;)^( )x^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )y^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )z^2)(psi))",
diff(psi, x, x)+diff(psi, y, y)+((diff(psi, z, z))*IS*THE*KENETIC*ENERGY*OF*THE)*PARTICLE

restart

psi(t, x, y, z)

psi(t, x, y, z)

(7)

Loading PDEtools

I*`&hbar;`*(diff(Ket(psi, t), t))

I*`&hbar;`*(diff(Ket(psi, t), t))

(8)

SElns := I*`&hbar;`*(diff(Ket(psi, t), t)); 'SElns'

SElns

(9)

SErhs1 := `&hbar;`^2*(diff(psi, t, x, x)+diff(psi, t, y, y)+diff(psi, t, z, z))/(2*m)

0

(10)

``

 

``

Classical physics example

KE = p^2/(2*m)

KE = (1/2)*p^2/m

(11)

KE = (p[x]^2+p[y]^2+p[z]^2)/(2*m)

KE = (1/2)*(p[x]^2+p[y]^2+p[z]^2)/m

(12)

QUANTUM MECHANICS

``

p[x] = `&hbar;`*(Diff(p[x], x))/(I)

p[x] = -I*`&hbar;`*(Diff(p[x], x))

(13)

 

p[x]^2 = Diff(rhs(p[x] = -I*`&hbar;`*(Diff(p[x], x))))

p[x]^2 = Diff(-I*`&hbar;`*(Diff(p[x], x)))

(14)

substituting each value of p[x], p[y],p[z]  IN EQ 11 is the KE

ONE VERY IMPORTANT SOLUTUION TO SE IS LISTED BELOW

psi(t, `#mover(mi("x"),mo("&rarr;"))`)= "Pi^(-3/(4)) sigma^(-3/(2))C(t)^(-3/(2))Exp((-1/(2))(((x)^(2))/(sigma^(2 )C(t)))+ ((i p *x-(i( p)^(2)(t/(`&hbar;`^())))/(2 m))/(C(t)))"

C(t) = 1 +  "(`i&hbar;` t))/((m sigma^(2))), sigma= initial position uncertainty of the particle,m,mass of particle"

```#mover(mi("p"),mo("&rarr;"))`=<p[x],p[y],p[z]>...just 3 Real no...this is NOT THE SAME AS EQ 14

There are 3 parmeters in the above eq σ (NOT PAULI), m ,`#mover(mi("p"),mo("&rarr;"))`

abs(psi(t, `#mover(mi("x"),mo("&rarr;"))`))^2 = 1/Pi^(3/2)Exp(-(`#mover(mi("x"),mo("&rarr;"))`-i*`#mover(mi("p"),mo("&rarr;"))`(t/m))^2/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2))/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)^(3/2)

int(abs(psi(t, `#mover(mi("x",fontweight = "bold"),mo("&rarr;",fontweight = "bold"))`))^2, V) = 1

THE ABOVE FUNCTION WILL BE A MAXIMUM WHEN `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t/m

distribution,

n. 1. (Statistics) the set of possible values of a random variable, or points in a sample space , considered in terms of their theoretical or observed frequency . 2. also called generalized function. a generalization of the concept of a function, defined as continuous linear functionals  over spaces of infinitely differentiable functions, introduced so that all continuous functions possess partial distributional derivatives (also called Schwartzian derivatives) that are again distributions. This leads to so-called weak solutions of differential equations and is of importance in the theory of partial differential equations ...

THE EQ YIEDS A GAUSSIAN "BELL SHAPE IN 2 D ONLY, CANNOT BE DRAWN 3D, 
abs(psi)^2*y*axis, `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t*x*axis/m, width = sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t and sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t = ((0*this)*will*equal*sigma*initial*uncertainity*of*the*position*of)*the*particle

t→∞ width = `#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m)

``

restart

with(Student[VectorCalculus])

with(VectorCalculus)

with(plots)

 

ln(1) := ts

ts

(15)

ts := 2

2

(16)

sigma := 4

4

(17)

h := 1

1

(18)

M := 1

1

(19)

P := 1

1

(20)

x

x

(21)

psi(x, t)

psi(x, t)

(22)

I = sqrt(-1)

I = I

(23)

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

h, I, ts, M

1, I, 2, 1

(24)

sigma^2

16

(25)

I*h*ts/M

2*I

(26)

 

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

2+2*I

2+2*I

(27)

(-1/2)*(x^2)

-(1/2)*x^2

(28)

"((-1/2)((x^2)/((sigma^2+(I*h*(t/M))))"

NULL

-(1/2)*x^2/(2+2*I)

(-1/8+(1/8)*I)*x^2

(29)

``

``

"Exp(((-1/2)((x^2)/((sigma^2+(I*h*(t/M)))))+(((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

NULL

I*P*x/h

I*x

(30)

 

I*P^2*t/((2*M)*h)

((1/2)*I)*t

(31)

I*x-((1/2)*I)*t

I*x-((1/2)*I)*t

(32)

"((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

``

NULL

I*h*t

I*t

(33)

sigma^2+M

17

(34)

1+I*t*(1/17)

1+((1/17)*I)*t

(35)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(36)

NULL

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(37)

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(38)

simplify(psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)))

psi(x, t) = exp(-I*(-2*x+t)*(I*t+34)/((2*I)*t+34))

 

Explore(psi(x, t) = exp(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(I, `-`(2*x)+t), VectorCalculus:-`+`(VectorCalculus:-`*`(I, t), 34)), 1/VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(2, I), t), 34)))), parameters = [[t = 0 .. 40, controller = slider], [x = -20 .. 80, controller = slider]], loop = never, size = NoUserValue, numeric = false, echoexpression = true)

(39)

with(plots)

implicitplot(abs(psi(x, ts*t)), Re(psi(x, ts*t)), Im(psi(x, ts*t)), x = -20 .. 80, scaling = constrained)

Error, (in plots/implicitplot) invalid input: lhs received Im(psi(x, 2*t)), which is not valid for its 1st argument, expr

 

NULL


 

Download Lec7QuantumWaveSE.mw
 

NULL

BELOW IS ADRESSING PARTICLE MOTION AND HOW ELECTRONS MOVE AROUND AND HOW MAGNETIC FIELDS AFFECTION THE MOTION OF ELECTRONS

 

PARTICLE MOTION "IGNORING SPIN" WILL COME BACK TO THAT

restart

with(Physics); interface(imaginaryunit = i)

Setup(hermitianoperators = {H, O__H, O__S}, realobjects = {`&hbar;`, m, t, x_}, combinepowersofsamebase = true, mathematicalnotation = true)

[combinepowersofsamebase = true, hermitianoperators = {H, O__H, O__S}, mathematicalnotation = true, realobjects = {`&hbar;`, m, t, x_}]

(1)

with(Physics[Vectors])

WAVE FUNCTION OF PARITCLE. t =time , x= some position vector

x_ = `<,>`(x, y, z)

x_ = Vector[column](%id = 36893489722226370188)

(2)

psi(t, x_)

psi(t, x_)

(3)

psi(t, x, y, z)

psi(t, x, y, z)

(4)

p_

p_

(5)

ψ is xome complex number with a real and imaginary number, the absolute value of abs(psi(t, x_))^2
`and`((is*the*probabilty*density*of*finding*the)*particle*at*postion*vector*x, at*time*t), ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, int(abs(psi(t, x_))^2, V) = 1

abs(psi(t, x_))^2

 

is*the^2*probabilty*density*of*finding*particle*at*postion*vector*x and at*time*t, ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, abs(psi(t, x_))^2*V = 1

(6)

THE ABOVE EQUATION IS TRUE IF THE WAVE FUNCTION IS "PROPERLY NORMALIZED"

THE WAVE FUNCTION EVOLVES IN TIME ACCORDING TO SCHRODINGER EQ

"`i&hbar;`(&PartialD;Psi)/(&PartialD;t)= -(`&hbar;`^(2))/(2 m)(((&PartialD;)^2)/((&PartialD;)^( )x^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )y^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )z^2)(psi))",
diff(psi, x, x)+diff(psi, y, y)+((diff(psi, z, z))*IS*THE*KENETIC*ENERGY*OF*THE)*PARTICLE

restart

psi(t, x, y, z)

psi(t, x, y, z)

(7)

Loading PDEtools

I*`&hbar;`*(diff(Ket(psi, t), t))

I*`&hbar;`*(diff(Ket(psi, t), t))

(8)

SElns := I*`&hbar;`*(diff(Ket(psi, t), t)); 'SElns'

SElns

(9)

SErhs1 := `&hbar;`^2*(diff(psi, t, x, x)+diff(psi, t, y, y)+diff(psi, t, z, z))/(2*m)

0

(10)

``

 

``

Classical physics example

KE = p^2/(2*m)

KE = (1/2)*p^2/m

(11)

KE = (p[x]^2+p[y]^2+p[z]^2)/(2*m)

KE = (1/2)*(p[x]^2+p[y]^2+p[z]^2)/m

(12)

QUANTUM MECHANICS

``

p[x] = `&hbar;`*(Diff(p[x], x))/(I)

p[x] = -I*`&hbar;`*(Diff(p[x], x))

(13)

 

p[x]^2 = Diff(rhs(p[x] = -I*`&hbar;`*(Diff(p[x], x))))

p[x]^2 = Diff(-I*`&hbar;`*(Diff(p[x], x)))

(14)

substituting each value of p[x], p[y],p[z]  IN EQ 11 is the KE

ONE VERY IMPORTANT SOLUTUION TO SE IS LISTED BELOW

psi(t, `#mover(mi("x"),mo("&rarr;"))`)= "Pi^(-3/(4)) sigma^(-3/(2))C(t)^(-3/(2))Exp((-1/(2))(((x)^(2))/(sigma^(2 )C(t)))+ ((i p *x-(i( p)^(2)(t/(`&hbar;`^())))/(2 m))/(C(t)))"

C(t) = 1 +  "(`i&hbar;` t))/((m sigma^(2))), sigma= initial position uncertainty of the particle,m,mass of particle"

```#mover(mi("p"),mo("&rarr;"))`=<p[x],p[y],p[z]>...just 3 Real no...this is NOT THE SAME AS EQ 14

There are 3 parmeters in the above eq σ (NOT PAULI), m ,`#mover(mi("p"),mo("&rarr;"))`

abs(psi(t, `#mover(mi("x"),mo("&rarr;"))`))^2 = 1/Pi^(3/2)Exp(-(`#mover(mi("x"),mo("&rarr;"))`-i*`#mover(mi("p"),mo("&rarr;"))`(t/m))^2/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2))/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)^(3/2)

int(abs(psi(t, `#mover(mi("x",fontweight = "bold"),mo("&rarr;",fontweight = "bold"))`))^2, V) = 1

THE ABOVE FUNCTION WILL BE A MAXIMUM WHEN `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t/m

distribution,

n. 1. (Statistics) the set of possible values of a random variable, or points in a sample space , considered in terms of their theoretical or observed frequency . 2. also called generalized function. a generalization of the concept of a function, defined as continuous linear functionals  over spaces of infinitely differentiable functions, introduced so that all continuous functions possess partial distributional derivatives (also called Schwartzian derivatives) that are again distributions. This leads to so-called weak solutions of differential equations and is of importance in the theory of partial differential equations ...

THE EQ YIEDS A GAUSSIAN "BELL SHAPE IN 2 D ONLY, CANNOT BE DRAWN 3D, 
abs(psi)^2*y*axis, `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t*x*axis/m, width = sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t and sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t = ((0*this)*will*equal*sigma*initial*uncertainity*of*the*position*of)*the*particle

t→∞ width = `#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m)

``

restart

with(Student[VectorCalculus])

with(VectorCalculus)

with(plots)

 

ln(1) := ts

ts

(15)

ts := 2

2

(16)

sigma := 4

4

(17)

h := 1

1

(18)

M := 1

1

(19)

P := 1

1

(20)

x

x

(21)

psi(x, t)

psi(x, t)

(22)

I = sqrt(-1)

I = I

(23)

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

h, I, ts, M

1, I, 2, 1

(24)

sigma^2

16

(25)

I*h*ts/M

2*I

(26)

 

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

2+2*I

2+2*I

(27)

(-1/2)*(x^2)

-(1/2)*x^2

(28)

"((-1/2)((x^2)/((sigma^2+(I*h*(t/M))))"

NULL

-(1/2)*x^2/(2+2*I)

(-1/8+(1/8)*I)*x^2

(29)

``

``

"Exp(((-1/2)((x^2)/((sigma^2+(I*h*(t/M)))))+(((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

NULL

I*P*x/h

I*x

(30)

 

I*P^2*t/((2*M)*h)

((1/2)*I)*t

(31)

I*x-((1/2)*I)*t

I*x-((1/2)*I)*t

(32)

"((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

``

NULL

I*h*t

I*t

(33)

sigma^2+M

17

(34)

1+I*t*(1/17)

1+((1/17)*I)*t

(35)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(36)

NULL

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(37)

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(38)

simplify(psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)))

psi(x, t) = exp(-I*(-2*x+t)*(I*t+34)/((2*I)*t+34))

 

Explore(psi(x, t) = exp(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(I, `-`(2*x)+t), VectorCalculus:-`+`(VectorCalculus:-`*`(I, t), 34)), 1/VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(2, I), t), 34)))), parameters = [[t = 0 .. 40, controller = slider], [x = -20 .. 80, controller = slider]], loop = never, size = NoUserValue, numeric = false, echoexpression = true)

(39)

with(plots)

implicitplot(abs(psi(x, ts*t)), Re(psi(x, ts*t)), Im(psi(x, ts*t)), x = -20 .. 80, scaling = constrained)

Error, (in plots/implicitplot) invalid input: lhs received Im(psi(x, 2*t)), which is not valid for its 1st argument, expr

 

NULL


 

Download Lec7QuantumWaveSE.mw
 

NULL

BELOW IS ADRESSING PARTICLE MOTION AND HOW ELECTRONS MOVE AROUND AND HOW MAGNETIC FIELDS AFFECTION THE MOTION OF ELECTRONS

 

PARTICLE MOTION "IGNORING SPIN" WILL COME BACK TO THAT

restart

with(Physics); interface(imaginaryunit = i)

Setup(hermitianoperators = {H, O__H, O__S}, realobjects = {`&hbar;`, m, t, x_}, combinepowersofsamebase = true, mathematicalnotation = true)

[combinepowersofsamebase = true, hermitianoperators = {H, O__H, O__S}, mathematicalnotation = true, realobjects = {`&hbar;`, m, t, x_}]

(1)

with(Physics[Vectors])

WAVE FUNCTION OF PARITCLE. t =time , x= some position vector

x_ = `<,>`(x, y, z)

x_ = Vector[column](%id = 36893489722226370188)

(2)

psi(t, x_)

psi(t, x_)

(3)

psi(t, x, y, z)

psi(t, x, y, z)

(4)

p_

p_

(5)

ψ is xome complex number with a real and imaginary number, the absolute value of abs(psi(t, x_))^2
`and`((is*the*probabilty*density*of*finding*the)*particle*at*postion*vector*x, at*time*t), ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, int(abs(psi(t, x_))^2, V) = 1

abs(psi(t, x_))^2

 

is*the^2*probabilty*density*of*finding*particle*at*postion*vector*x and at*time*t, ASSUME*SOME*POSITION*VECTOR*x, with*an*infintesmial*cube*around*it, infintesimal*volume*dV, PROBABILY*DENSITY*IS*abs(psi(t, x_))^2*dV, abs(psi(t, x_))^2*V = 1

(6)

THE ABOVE EQUATION IS TRUE IF THE WAVE FUNCTION IS "PROPERLY NORMALIZED"

THE WAVE FUNCTION EVOLVES IN TIME ACCORDING TO SCHRODINGER EQ

"`i&hbar;`(&PartialD;Psi)/(&PartialD;t)= -(`&hbar;`^(2))/(2 m)(((&PartialD;)^2)/((&PartialD;)^( )x^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )y^2)(psi)+((&PartialD;)^2)/((&PartialD;)^( )z^2)(psi))",
diff(psi, x, x)+diff(psi, y, y)+((diff(psi, z, z))*IS*THE*KENETIC*ENERGY*OF*THE)*PARTICLE

restart

psi(t, x, y, z)

psi(t, x, y, z)

(7)

Loading PDEtools

I*`&hbar;`*(diff(Ket(psi, t), t))

I*`&hbar;`*(diff(Ket(psi, t), t))

(8)

SElns := I*`&hbar;`*(diff(Ket(psi, t), t)); 'SElns'

SElns

(9)

SErhs1 := `&hbar;`^2*(diff(psi, t, x, x)+diff(psi, t, y, y)+diff(psi, t, z, z))/(2*m)

0

(10)

``

 

``

Classical physics example

KE = p^2/(2*m)

KE = (1/2)*p^2/m

(11)

KE = (p[x]^2+p[y]^2+p[z]^2)/(2*m)

KE = (1/2)*(p[x]^2+p[y]^2+p[z]^2)/m

(12)

QUANTUM MECHANICS

``

p[x] = `&hbar;`*(Diff(p[x], x))/(I)

p[x] = -I*`&hbar;`*(Diff(p[x], x))

(13)

 

p[x]^2 = Diff(rhs(p[x] = -I*`&hbar;`*(Diff(p[x], x))))

p[x]^2 = Diff(-I*`&hbar;`*(Diff(p[x], x)))

(14)

substituting each value of p[x], p[y],p[z]  IN EQ 11 is the KE

ONE VERY IMPORTANT SOLUTUION TO SE IS LISTED BELOW

psi(t, `#mover(mi("x"),mo("&rarr;"))`)= "Pi^(-3/(4)) sigma^(-3/(2))C(t)^(-3/(2))Exp((-1/(2))(((x)^(2))/(sigma^(2 )C(t)))+ ((i p *x-(i( p)^(2)(t/(`&hbar;`^())))/(2 m))/(C(t)))"

C(t) = 1 +  "(`i&hbar;` t))/((m sigma^(2))), sigma= initial position uncertainty of the particle,m,mass of particle"

```#mover(mi("p"),mo("&rarr;"))`=<p[x],p[y],p[z]>...just 3 Real no...this is NOT THE SAME AS EQ 14

There are 3 parmeters in the above eq σ (NOT PAULI), m ,`#mover(mi("p"),mo("&rarr;"))`

abs(psi(t, `#mover(mi("x"),mo("&rarr;"))`))^2 = 1/Pi^(3/2)Exp(-(`#mover(mi("x"),mo("&rarr;"))`-i*`#mover(mi("p"),mo("&rarr;"))`(t/m))^2/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2))/(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)^(3/2)

int(abs(psi(t, `#mover(mi("x",fontweight = "bold"),mo("&rarr;",fontweight = "bold"))`))^2, V) = 1

THE ABOVE FUNCTION WILL BE A MAXIMUM WHEN `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t/m

distribution,

n. 1. (Statistics) the set of possible values of a random variable, or points in a sample space , considered in terms of their theoretical or observed frequency . 2. also called generalized function. a generalization of the concept of a function, defined as continuous linear functionals  over spaces of infinitely differentiable functions, introduced so that all continuous functions possess partial distributional derivatives (also called Schwartzian derivatives) that are again distributions. This leads to so-called weak solutions of differential equations and is of importance in the theory of partial differential equations ...

THE EQ YIEDS A GAUSSIAN "BELL SHAPE IN 2 D ONLY, CANNOT BE DRAWN 3D, 
abs(psi)^2*y*axis, `#mover(mi("x"),mo("&rarr;"))` = `#mover(mi("p"),mo("&rarr;"))`*t*x*axis/m, width = sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t and sqrt(sigma^2+(`#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m))^2)*so*at*t = ((0*this)*will*equal*sigma*initial*uncertainity*of*the*position*of)*the*particle

t→∞ width = `#msup(mi("&hbar;"),mo("&InvisibleTimes;"))`*t/(sigma*m)

``

restart

with(Student[VectorCalculus])

with(VectorCalculus)

with(plots)

 

ln(1) := ts

ts

(15)

ts := 2

2

(16)

sigma := 4

4

(17)

h := 1

1

(18)

M := 1

1

(19)

P := 1

1

(20)

x

x

(21)

psi(x, t)

psi(x, t)

(22)

I = sqrt(-1)

I = I

(23)

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

h, I, ts, M

1, I, 2, 1

(24)

sigma^2

16

(25)

I*h*ts/M

2*I

(26)

 

about(I)

I:
  All numeric values are properties as well as objects.
  Their location in the property lattice is obvious,
  in this case complex(extended_numeric).
 

 

2+2*I

2+2*I

(27)

(-1/2)*(x^2)

-(1/2)*x^2

(28)

"((-1/2)((x^2)/((sigma^2+(I*h*(t/M))))"

NULL

-(1/2)*x^2/(2+2*I)

(-1/8+(1/8)*I)*x^2

(29)

``

``

"Exp(((-1/2)((x^2)/((sigma^2+(I*h*(t/M)))))+(((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

NULL

I*P*x/h

I*x

(30)

 

I*P^2*t/((2*M)*h)

((1/2)*I)*t

(31)

I*x-((1/2)*I)*t

I*x-((1/2)*I)*t

(32)

"((I *P* (x/h))- (I* ((P^2)/(2*M))*(t/h))/((1+(((I*h*t))/((M+sigma^2))))"

``

NULL

I*h*t

I*t

(33)

sigma^2+M

17

(34)

1+I*t*(1/17)

1+((1/17)*I)*t

(35)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)

(36)

NULL

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(37)

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t))

(38)

simplify(psi(x, t) = exp(I*x-((1/2)*I)*t+(I*x-((1/2)*I)*t)/(1+((1/17)*I)*t)))

psi(x, t) = exp(-I*(-2*x+t)*(I*t+34)/((2*I)*t+34))

 

Explore(psi(x, t) = exp(VectorCalculus:-`-`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(I, `-`(2*x)+t), VectorCalculus:-`+`(VectorCalculus:-`*`(I, t), 34)), 1/VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(2, I), t), 34)))), parameters = [[t = 0 .. 40, controller = slider], [x = -20 .. 80, controller = slider]], loop = never, size = NoUserValue, numeric = false, echoexpression = true)

(39)

with(plots)

implicitplot(abs(psi(x, ts*t)), Re(psi(x, ts*t)), Im(psi(x, ts*t)), x = -20 .. 80, scaling = constrained)

Error, (in plots/implicitplot) invalid input: lhs received Im(psi(x, 2*t)), which is not valid for its 1st argument, expr

 

NULL


 

Download Lec7QuantumWaveSE.mw

 

 

I am trying to plot a Runge-Kutta method for 1+ tsin(tx). When ever I try to do the plot data command an empty graph shows up. I noticed that some of my values from the algorithm did not calculate properly. How do I fix this problem? This is what I typed in for the calculations. 

f := (t, x) -> 1 + t*sin(x);
t[0] := 0;x[0] := 0;
h := 0.1;
 

for n to 20 do
    t[n] := n*h;
    m1 := f(t[n - 1], x[n - 1]);
    m2 := f(t[n - 1] + h/2, x[n - 1] + m1*h/2);
    m3 := f(t[n - 1] + h/2, x[n - 1] + m2*h/2);
    m4 := f(t[n - 1] + h, h*m3 + x[n - 1]);
    x[n] := x[n - 1] + h/6*(m1 + 2*m2 + 2*m3 + m4);
end;
 

Hi

I am trying to follow this paper

http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf

Lets start with the easier problem, equal poles. Assume that the length of the cable is 120m and the two poles have equal height of 50m. Our goal is to determine the minimum distance between the two poles that will prevent the cable from touching the ground.

I was trying to get Maple to agree with their derived formula, namely

y(x)= 11*cosh(1/11*x) - 61,

but I think I have not set the IC's correctly. or provided for the length of the cable.

restart:
int(sqrt(1+diff(y(t),t)^2),t=0..x)=120/2

//can't solve the above directly, or maybe someone clever here can

//a is a constant
DIV := diff(y(x), x, x) = a*sqrt(1 + diff(y(x), x)^2);
RV := y(0) = 0, D(y)(0) = -50;
dsolve({DIV});
Opl := dsolve({DIV, RV}, y(x));
allvalues(%)
 

 

Hi I have experienced another Maple 2021 error with those of my students who Maple 2021 Mac edition. 

Lets say their have saved a .mw on their main drive and tries to open the file from inside Maple. Maple gives an error like "file cannot be opened - please try to another". This also happens when trying to open the file from outside Maple. 

This never happens on the Windows version. So any idea what could be causing this ?

 

 

 

 

 

"D1(s,t) :=P- (alpha1-beta*S) +  alpha2 + beta2 *q(t)^();"

proc (s, t) options operator, arrow; P+beta*S-alpha1+alpha2+beta2*q(t) end proc

(1)

"(->)"

dem

(2)

``

ode1 := diff(q(t), t)+theta*q(t)/(1+N-t) = -D1(s, t)

diff(q(t), t)+theta*q(t)/(1+N-t) = -P-beta*S+alpha1-alpha2-beta2*q(t)

(3)

fn1 := q(t)

q(t)

(4)

ic1 := q(T) = 0

q(T) = 0

(5)

sol1 := simplify(dsolve({ic1, ode1}, fn1))

q(t) = (-S*beta-P+alpha1-alpha2)*(Int(exp(beta2*_z1)*(1+N-_z1)^(-theta), _z1 = T .. t))*exp(-beta2*t)*(1+N-t)^theta

(6)

NULL

Download data.mw

Hello all. I'm trying to solve the following first-order differential equation. 

Please help in understanding why the equation (6) doesn't contain proper solution for the function q(t) on solving the ode1 with the given initial condition

How (can I?) display the value in a legend in Engineering format -- 10^3, 10^-6, etc?

Lres := 1/((2*Pi*freq)^2*Cres);
ftest := 10e6;
p1 := plot(eval(subs(freq = ftest, Lres)), Cres = 0.10000000 .. 0.10000000, labels = [Cres, 'Lres'], legend = ftest, color = red, title = 'Inductance*Value*as*a*Function*of*Resonant*Capacitance', axis = [gridlines = [default]]);

I would like the legend to display 10^6 rather than 1^7.

I've tried changing the default number format for the whole worksheet to Engineering, but that doesn't seem to apply to legends.

 

thank you.

Hi,

I'd like to know, if it is possible to define any sort of range for parameters in NonlinearFit. E. g. I know that one of parameters should be somewhere between 0.2 - 0.4. I know there is a possibility of initalvalues, but using it doesn't lead into this range.

Thanks.

Hi. So my question is how can I get Square brackets on the phone app in calculations or is it possible?

 

 

In a french magazine written by High Schools teachers I found this problem:

let a, b, p, q four strictly positive integers such that a > b^2 and p > q+1;
find 4-tuples (a, b, p, q) such that 

(a^2 - b^4) = p!/q!

Given the source of this problem I suspect that there is a trick to answering this question.
After some hours spent, I have found no general method to solve it, only a few solutions (first one and second one are almost obvious), for instance

rel := a^2 - b^4 = p!/q!:

eval(rel, [a= 5, b=1, q=1, p=4]);   
eval(rel, [a=11, b=1, q=1, p=5]);
eval(rel, [a=71, b=1, q=1, p=7]);
eval(rel, [a= 2, b=1, q=2, p=3]);
eval(rel, [a=19, b=1, q=2, p=6]);
eval(rel, [a=21, b=3, q=2, p=6]);

Do you have any idea how to solve this problem?
Could it be handled by Maple (without a systematic exploration of a part of N^4)?

Thanks in advance

lets say we have one or two lines 

y=2x-4 and y = -2x+4 is it possible to get Maple to illustrate the angle between these two lines in a plot? Or the angle of inclination in respect to the x-axes for them individually? 

kindly help me to find the inverse Laplace of this function. I tried but maple leaves the integral unevaluated.
 

restart

with(inttrans)

expr := exp(a-sqrt(a^2+b*s))/s

exp(a-(a^2+b*s)^(1/2))/s

(1)

`assuming`([invlaplace(expr, s, t)], [b > 0])

(1/2)*(b/Pi)^(1/2)*(int(exp(-a^2*_U1/b+a-(1/4)*b/_U1)/_U1^(3/2), _U1 = 0 .. t))

(2)

NULL


 

Download invrslplc.mw

how can revision of error in 

restart;
u0 := proc (x) options operator, arrow; 1+2*x end proc; h := 0;
for k from 0 to 5 do U := proc (k, h) options operator, arrow; eval((diff(u0(x), [`$`(x, k)]))/factorial(k), x = 0) end proc end do;
m := h+1;
for k from 0 to 5 do U := proc (k, h) options operator, arrow; (sum(sum(U(r, h-s)*U(k-r, s), s = 0 .. h), r = 0 .. k)+(k+1)*U(k, h))/m end proc end do;
U(0, 1);
Error, (in U) too many levels of recursion

 

I have the following expression.

Ps = (x - 600)(15000 + 400*(y - 4000)/2000 + 15000*0.40*(850 - x)/100) - y

Maple will evaluate this to:

Ps = (x - 600)(15000 + 400*(y - 4000)/2000 + 15000*0.40*(850 - x)/100) - y

Screenshot:

Plotting these two in 2D on Desmos to demonstrate: https://www.desmos.com/calculator/tvp4rbzxzp

These two are not the same expression. Is Maple broken or am I doing something wrong?

Hello. Please help me solve the ODE system

ODU_v2.mw
 

restart

with(linalg):

r1 := 1:

1

 

0.1111110000e-2

 

0

 

1920.000000+0.7407400000e-3*I

(1)

J := proc (n, x) options operator, arrow; BesselJ(n, x) end proc:

nsize := floor(2*k)+1;

3

(2)

n := 1; A1 := matrix([[(lambda(r)+2*mu(r))*r^2, 0], [0, mu(r)*r^2]]); B1 := matrix([[(diff(lambda(r), r)+2*(diff(mu(r), r)))*r^2+(lambda(r)+2*mu(r))*r, I*n*(lambda(r)+mu(r))*r], [I*n*(lambda(r)+mu(r))*r, (diff(mu(r), r))*r^2+mu(r)*r]]); C1 := matrix([[(diff(lambda(r), r))*r-lambda(r)-(n^2+2)*mu(r)+omega^2*rho(r)*r^2, I*n*((diff(lambda(r), r))*r-lambda(r)-3*mu(r))], [I*n*((diff(mu(r), r))*r+lambda(r)+3*mu(r)), -(diff(mu(r), r))*r-n^2*lambda(r)-(2*n^2+1)*mu(r)+omega^2*rho(r)*r^2]]); U := vector([U1(r), U2(r)]); DU := vector([diff(U1(r), r), diff(U2(r), r)]); D2U := vector([diff(U1(r), `$`(r, 2)), diff(U2(r), `$`(r, 2))]); T1 := multiply(A1, D2U); T2 := multiply(B1, DU); T3 := multiply(C1, U); prav := evalm(T1+T2+T3); pr1 := prav[1]; pr2 := prav[2]; p1 := evalc(Re(pr1)); p2 := evalc(Im(pr1)); p3 := evalc(Re(pr2)); p4 := evalc(Im(pr2)); WWVV := evalf(subs(x = k*r1, H(n, x)))*evalf(subs(x = k2*r1, H(n, x)))*n^2-evalf(subs(x = k*r1, DH(n, x)))*evalf(subs(x = k2*r1, DH(n, x)))*k*k2*r1^2; `&alpha;v1` := I*evalf(subs(x = k2*r1, DH(n, x)))*k2*omega*r1^2/WWVV; `&alpha;v2` := -evalf(subs(x = k2*r1, H(n, x)))*n*omega*r1/WWVV; `&alpha;v3` := (evalf(subs(x = k*r1, DJ(n, x)))*evalf(subs(x = k2*r1, DH(n, x)))*I^n*k*k2*r1^2-I^n*n^2*evalf(subs(x = k*r1, J(n, x)))*evalf(subs(x = k2*r1, H(n, x))))/WWVV; `&alpha;v4` := evalf(subs(x = k*r1, H(n, x)))*r1*n*omega/WWVV; `&alpha;v5` := -I*evalf(subs(x = k*r1, DH(n, x)))*r1^2*k*omega/WWVV; `&alpha;v6` := I*I^n*n*k*r1*(evalf(subs(x = k*r1, DJ(n, x)))*evalf(subs(x = k*r1, H(n, x)))-evalf(subs(x = k*r1, DH(n, x)))*evalf(subs(x = k*r1, J(n, x))))/WWVV; gv1 := rho1*(-evalf(subs(x = k*r1, D2H(n, x)))*k^2*r^2*(4*nu+3*xi)-3*evalf(subs(x = k*r1, DH(n, x)))*k*r1*xi+evalf(subs(x = k*r1, H(n, x)))*(-4*k^2*r1^2*nu-3*k^2*r1^2*xi+(3*I)*omega*r1^2-2*n^2*nu+3*n^2*xi))/(3*r1^2); gv2 := (6*rho1/(3*r1^2)*I)*n*nu*(evalf(subs(x = k2*r1, H(n, x)))-k2*r1*evalf(subs(x = k2*r1, DH(n, x)))); gv3 := rho1*(-I^n*evalf(subs(x = k*r1, D2J(n, x)))*k*r1^2*(4*nu+3*xi)+I^n*evalf(subs(x = k*r1, DJ(n, x)))*k*r1*(2*nu-3*xi)+I^n*evalf(subs(x = k*r1, J(n, x)))*(-4*k^2*r1^2*nu-3*k^2*r1^2*xi+(3*I)*omega*r1^2-2*n^2*nu+3*n^2*xi))/(3*r1^2); gv4 := (2*nu*rho1/r1^2*I)*n*(evalf(subs(x = k*r1, H(n, x)))-evalf(subs(x = k*r1, DH(n, x)))*k*r1); gv5 := nu*rho1*(evalf(subs(x = k2*r1, D2H(n, x)))*k2^2*r1^2-evalf(subs(x = k2*r1, D2H(n, x)))*k2*r1+evalf(subs(x = k2*r1, H(n, x)))*n^2)/r1^2; gv6 := (2*nu*rho1/r1^2*I)*n*I^n*(evalf(subs(x = k*r1, J(n, x)))-k*r1*evalf(subs(x = k*r1, DJ(n, x)))); E := matrix([[`&alpha;v1`*gv1+`&alpha;v4`*gv2+lambda(r1)/r1, `&alpha;v2`*gv1+`&alpha;v4`*gv2+I*n*lambda(r1)/r1], [`&alpha;v1`*gv4+`&alpha;v4`*gv5+I*n*mu(r1)/r1, `&alpha;v2`*gv4+`&alpha;v5`*gv5-mu(r1)/r1]]); G := vector([-gv1*`&alpha;v3`-gv2*`&alpha;v6`-gv3, -gv4*`&alpha;v3`-gv5*`&alpha;v6`-gv6]); e1 := (lambda2*n^2*evalf(subs(x = kl*r2, J(n, x)))-kl^2*r2^2*evalf(subs(x = kl*r2, D2J(n, x)))*(lambda2+2*mu2)-kl*lambda2*r2*evalf(subs(x = kl*r2, DJ(n, x))))/r2^2; e2 := (2*mu2*I)*n*(evalf(subs(x = kt*r2, J(n, x)))-kt*r2*evalf(subs(x = kt*r2, DJ(n, x))))/r2^2; e3 := (I*n*2)*(evalf(subs(x = kl*r2, J(n, x)))-kl*r2*evalf(subs(x = kl*r2, DJ(n, x))))/r2^2; e4 := (kt^2*r2^2*evalf(subs(x = kt*r2, D2J(n, x)))-kt*r2*evalf(subs(x = kt*r2, DJ(n, x)))+n^2*evalf(subs(x = kt*r2, J(n, x))))/r2^2; gamma1 := kt*r2*evalf(subs(x = kt*r2, DJ(n, x)))/WW; gamma2 := I*n*evalf(subs(x = kt*r2, J(n, x)))/WW; gamma3 := I*n*evalf(subs(x = kl*r2, J(n, x)))/WW; gamma4 := -kl*r2*evalf(subs(x = kl*r2, DJ(n, x)))/WW; WW := (kl*r2^2*evalf(subs(x = kl*r2, DJ(n, x)))*kt*evalf(subs(x = kt*r2, DJ(n, x)))-n^2*evalf(subs(x = kl*r2, J(n, x)))*evalf(subs(x = kt*r2, J(n, x))))/r2; F := matrix([[r2^2*(gamma1*e1+gamma3*e2+lambda(r2)/r2), r2^2*(gamma2*e1+gamma4*e2+I*n*lambda(r2)/r2)], [mu2*r2^2*(gamma1*e3+gamma3*e4+I*n*mu(r2)/(mu2*r2)), mu2*r2^2*(gamma2*e3+gamma4*e4-mu(r2)/(mu2*r2))]]); Ur1 := vector([U1(r1), U2(r1)]); Ur2 := vector([U1(r2), U2(r2)]); DUr1 := vector([Dx1(r1)+I*Dy1(r1), Dx2(r1)+I*Dy2(r1)]); DUr2 := vector([Dx1(r2)+I*Dy1(r2), Dx2(r2)+I*Dy2(r2)]); CCR1 := multiply(A1, DUr1); CCR2 := multiply(E, Ur1); CR := evalm(CCR1+CCR2); CCR11 := multiply(A1, DUr2); CCR22 := multiply(F, Ur2); CR2 := evalm(CCR11+CCR22); ggr1 := expand(evalc(Re(CR[1]))); ggr2 := expand(evalc(Im(CR[1]))); ggr3 := expand(evalc(Re(CR[2]))); ggr4 := expand(evalc(Im(CR[2]))); ggr5 := expand(evalc(Re(CR2[1]))); ggr6 := expand(evalc(Im(CR2[1]))); ggr7 := evalc(Re(CR2[2])); ggr8 := evalc(Im(CR2[2])); gr1 := subs(Dx1(r1) = (D(x1))(r1), Dx2(r1) = (D(x2))(r1), Dy1(r1) = (D(y1))(r1), Dy2(r1) = (D(y2))(r1), r = r1, ggr1); gr2 := subs(Dx1(r1) = (D(x1))(r1), Dx2(r1) = (D(x2))(r1), Dy1(r1) = (D(y1))(r1), Dy2(r1) = (D(y2))(r1), r = r1, ggr2); gr3 := subs(Dx1(r1) = (D(x1))(r1), Dx2(r1) = (D(x2))(r1), Dy1(r1) = (D(y1))(r1), Dy2(r1) = (D(y2))(r1), r = r1, ggr3); gr4 := subs(Dx1(r1) = (D(x1))(r1), Dx2(r1) = (D(x2))(r1), Dy1(r1) = (D(y1))(r1), Dy2(r1) = (D(y2))(r1), r = r1, ggr4); gr5 := subs(Dx1(r2) = (D(x1))(r2), Dx2(r2) = (D(x2))(r2), Dy1(r2) = (D(y1))(r2), Dy2(r2) = (D(y2))(r2), r = r2, ggr5); gr6 := subs(Dx1(r2) = (D(x1))(r2), Dx2(r2) = (D(x2))(r2), Dy1(r2) = (D(y1))(r2), Dy2(r2) = (D(y2))(r2), r = r2, ggr6); gr7 := subs(Dx1(r2) = (D(x1))(r2), Dx2(r2) = (D(x2))(r2), Dy1(r2) = (D(y1))(r2), Dy2(r2) = (D(y2))(r2), r = r2, ggr7); gr8 := subs(Dx1(r2) = (D(x1))(r2), Dx2(r2) = (D(x2))(r2), Dy1(r2) = (D(y1))(r2), Dy2(r2) = (D(y2))(r2), r = r2, ggr8); sys := p1 = 0, p2 = 0, p3 = 0, p4 = 0; Inits := gr3 = evalc(Re(G[2])), gr4 = evalc(Im(G[2])), gr1 = evalc(Re(G[1])), gr2 = evalc(Im(G[1])), gr5 = 0, gr6 = 0, gr7 = 0, gr8 = 0; dde := dsolve({Inits, sys}, numeric, [x1(r), x2(r), y1(r), y2(r)], method = bvp[trapdefer], 'maxmesh' = 5000)

1

 

5860000000.*r^2*(diff(diff(x1(r), r), r))+5860000000.*r*(diff(x1(r), r))-4880000000.*r*(diff(y2(r), r))+(-6840000000.+0.1972224000e11*r^3-0.1380556800e11*r^2)*x1(r)-(15217.76256*r^3-10652.43379*r^2)*y1(r)+6840000000.*y2(r) = 0, 5860000000.*r^2*(diff(diff(y1(r), r), r))+5860000000.*r*(diff(y1(r), r))+4880000000.*r*(diff(x2(r), r))+(15217.76256*r^3-10652.43379*r^2)*x1(r)+(-6840000000.+0.1972224000e11*r^3-0.1380556800e11*r^2)*y1(r)-6840000000.*x2(r) = 0, 980000000.0*r^2*(diff(diff(x2(r), r), r))-4880000000.*r*(diff(y1(r), r))+980000000.0*r*(diff(x2(r), r))-6840000000.*y1(r)+(-6840000000.+0.1972224000e11*r^3-0.1380556800e11*r^2)*x2(r)-(15217.76256*r^3-10652.43379*r^2)*y2(r) = 0, 980000000.0*r^2*(diff(diff(y2(r), r), r))+4880000000.*r*(diff(x1(r), r))+980000000.0*r*(diff(y2(r), r))+6840000000.*x1(r)+(15217.76256*r^3-10652.43379*r^2)*x2(r)+(-6840000000.+0.1972224000e11*r^3-0.1380556800e11*r^2)*y2(r) = 0

 

980000000.0*(D(x2))(1)-3407670.437*x1(1)-979699593.0*y1(1)-982493864.9*x2(1)+2501551.625*y2(1) = -1147.143928, 980000000.0*(D(y2))(1)+979699593.0*x1(1)-3407670.437*y1(1)-2501551.625*x2(1)-982493864.9*y2(1) = 522.0509891, 5860000000.*(D(x1))(1)+1012610130.*x1(1)+3433520814.*y1(1)-3395293.932*x2(1)-3899703885.*y2(1) = 1553476.957-0.8860949e-3*r^2, 5860000000.*(D(y1))(1)-3433520814.*x1(1)+1012610130.*y1(1)+3899703885.*x2(1)-3395293.932*y2(1) = 582234.6500+.6073438988*r^2, 3750400000.*(D(x1))(.8)-0.1805979289e11*x1(.8)-3057.354840*y1(.8)+182.8516896*x2(.8)+0.2220128109e11*y2(.8) = 0, 3750400000.*(D(y1))(.8)+3057.354840*x1(.8)-0.1805979289e11*y1(.8)-0.2220128109e11*x2(.8)+182.8516896*y2(.8) = 0, 627200000.0*(D(x2))(.8)-182.8520640*x1(.8)-0.2610528071e11*y1(.8)-0.2508771663e11*x2(.8)-607.0797125*y2(.8) = 0, 627200000.0*(D(y2))(.8)+0.2610528071e11*x1(.8)-182.8520640*y1(.8)+607.0797125*x2(.8)-0.2508771663e11*y2(.8) = 0

 

Error, (in dsolve/numeric/BVPSolve) unable to store '-HFloat(8.860193192958832e-4)+0.8860949e-3*r^2' when datatype=float[8]

 

``


 

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