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mz6687

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These are questions asked by mz6687

need assistance in finding a way...

mz6687 40 Maple 2022
substitution homework simplification
October 11 2024
0 6

I have encountered an issue: eq1 is not satisfied, though eq2 is satisfied for the parametric value (10). I need assistance in finding a way to ensure that both equations are satisfied simultaneously. Please provide guidance or suggest a potential approach for addressing this issue.verf_kk.mw

How can I substitute equation (5) into e...

mz6687 40 Maple 2022
substitution prime-derivative-notation
October 02 2024
1 0

How can I substitute equation (5) into equation (4) to obtain the final form [see image in BE.mw]?

Additionally, how can I use subscript notation for derivatives, such as expressing diff(f(tau,sigma), tau)  as f[tau]​?

By using the 'declare' command in Maple, one can utilize subscript notation. However, in this case, the function must be written in terms of τ and σ on each step.

How to collect coefficients?...

mz6687 40 Maple 2022
coefficients incomplete-question
September 26 2024
1 0

How to collect coefficients of eta^j, j=0,1 from (7)?

> 

restart
> 

with(LinearAlgebra)
> 

with(plots)
> 

with(Physics)
> 

interface(showassumed = 0)
> 

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)
> 

quantumOperators := {H, Id, Mqu, Mqu1, Theta, X, X1}

{H, Id, Mqu, Mqu1, Theta, X, X1}

 (2)
> 

Setup(quantumoperators = quantumOperators)

[quantumoperators = {H, Id, Mqu, Mqu1, Theta, X, X1}]

 (3)
> 

assume(x::real); assume(t::real)
> 

alias(q = q(x, t), qb = qb(x, t), r = r(x, t), rb = rb(x, t), psi = psi(x, t), phi = phi(x, t), g = g(x, t), gb = gb(x, t), H = H(x, t), X = X(x, t), X1 = X1(x, t), Theta = Theta(x, t), eta = eta(t), Mqu = Mqu(x, t))

q, qb, r, rb, psi, phi, g, gb, H, X, X1, Theta, eta, Mqu

 (4)
> 

``
> 

NULL
> 

D1 := (Id*eta-H).X

eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X)

 (5)
> 

D2 := diff(D1, x); D3 := subs({diff(X, x) = Mqu}, D2)

eta*Physics:-`*`(Id, diff(X, x))-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, diff(X, x))

  

eta*Physics:-`*`(Id, Mqu)-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, Mqu)

 (6)
> 

D3+D1 = D1*Mqu1

eta*Physics:-`*`(Id, Mqu)-Physics:-`*`(diff(H, x), X)-Physics:-`*`(H, Mqu)+eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X) = Physics:-`*`(eta*Physics:-`*`(Id, X)-Physics:-`*`(H, X), Mqu1)

 (7)
> 

collect(coeff, eta, 1)

1

 (8)
> 

collect(coeff, eta, 0)

0

 (9)
 

NULL

Download coefff.mw

How to find the dispersion relation?...

mz6687 40 Maple 2022
eigenvalues
September 16 2024
1 0

How to find the dispersion relation (9). Although I calculated the dispersion relation (see Eq. (3) in DR_1.mw), it is not consistent as in the image. 

 

temporal term disappears from the denomi...

mz6687 40 Maple 2022
simplify denominator
August 07 2024
1 0

Since the temporal term disappears from the denominator for any values of the parameters, I am puzzled. Why is this happening? It seems I might be missing something. When I consider one of the terms (named 'opnumeric') in the denominator and assign parametric values, the temporal term is present. However, when looking at the whole expression, the temporal term is absent in the denominator (named 'den1numeric'). How can this be resolved? numericden.mw

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