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Partial rectification for the Physics:-Simplify and Physics:-Library:-SortProducts procedures dealing with Fermi annihilation/creation operators

This post will be useful for physicists dealing with Fermi annihilation/creation operators. Physics Package provides plenty of powerful tools for quantum operators handling, however some of them often fail to render correct result.  In particular incorrect behaviour with respect to Fermi annihilation/creation operators is observed for routines Simplify and SortProducts.  In this post I present my procedures S*implifyFermionicOperators and SortProductsFermi which partially solve these issues.

Problems with Physics Package routines

   

Short explanation of custom routines SimplifyFermionicOperators and SortProductsFermi

   

"Details for SimplifyFermionicOperators(z,prefix)"

   

"Details for SortProductsFermi(x,L,prefix)"

   

Weak points

   

Final notes

   


Download FermiCreationAnnihilation.mw

Hello.
I am trying to extract the terms that are a product of a commutative part and an operator part from the input expression. That is I am trying to extract a terms like a*A.B where A and B are quantum pperators.

I am trying to do it by creating corresponding structured type:

restart; 
with(Physics);
Physics[Setup](op = {A, B}, quiet);

`type/ProdComOp` := `&*`(commutative, specfunc(anything, Physics:-`*`));
z0 := u*A.B-A+k*B+B.A.B+g;
z1 := z0+v*A.B.A;
S1 := indets(z1, ProdComOp);

and all it is Ok. The result is 
But if

z2 := z0-v*A.B.A; 
S2 := indets(z2, ProdComOp);

then
however I expected to receive the same as S1.

How to handle the sign of the commutative part? Thank you.

Hello Dears

I have this equation

                                          (Napla)^4 * F(x,y) + k^2 *  (Napla)^2 * F(x,y)= 0,      (1)

which may be written as a non-homgeneous Helmholtz equation as

                                          (Napla)^2 * F(x,y) + k^2 * F(x,y)= g(x,y),                (2)

where the function g(x,y) is a harmonic function and (Napla)^2 is the laplace's operator in two dimension.

Can Maple solve equation (1), it will be better. If not may be solve equation (2).

 

I am trying the following:

restart; 
with(Physics);
with(Library);
Setup(mathematicalnotation = true);
Setup(op = A);
assume(n::integer);

type(A^n, Physics:-`^`(PhysicsType:-ExtendedQuantumOperator, integer));
type(A^n, PhysicsType:-ExtendedQuantumOperator^integer);

the result is

false
false

However, I expected to get true in both cases. How to construct correct type for A^n?
Thank you.

https://drive.google.com/file/d/0B2D69u2pweEvaUNnVWdXbm9WT3c/edit?usp=sharing

for base 10

1 op1 5 = 

        01

op1   12

_________

first digit of first number 1     = 1

first digit of second number 1 = 2

 then find 12 in logic table, it is 1, separation is 1 means move the value 1

to left 1 digit become 10

convert 10 back from base 3 to base 10, it is 3

how to construct this unknown name operator table with the custom logic table Min, Except, Diff

based on the operation described

 

no matter the logic table is correct or not, hope to mechanize these calculation steps for developing 3 operation table for base 10 quickly.

is it possible to develop a new kind of algebra with 3 new operators with the use of 3 operation table?

 

 

I am newbie in Maple, and trying to understand when to use operator `if` as I see in some code vs. normal if. This is in context if using map()

I noticed I can write

A:=[seq(i,i=1..10)];
f:=x->x^2;
map(x->`if`(x<5,f(x),NULL),A);

or

map(x->if x<5 then f(x) fi,A);

And they both work the same. When should one use `if` vs. if? with the case of `if` I had to give a third argument NULL for the else part, while with using direct "if", I did not have to give the "else" part.

Also, suppose I want to use  IF .. THEN .. ELIF ... FI, then how would this be done using the operator syntax? in normal "if", I can write

A:=[seq(i,i=1..10)];
f:=x->x^2;
map(x->if x<5 then f(x) elif x=5 then x else x-1 fi,A);

Actually if I understand better when `if` is meant to be used vs. where the normal "if", I might understand more its use. 

 

ps. I did look at the help here but did not see it recommend when to use over the other (unless I overlooked it)

 

 

 

 

Dear all,

It's very convenient to define a DE or PDE through Differential Operator D, for example,

((D[1, 1]+D[1, 2]+D[2, 2])(z))(x, y) = exp(x)*sin(y)

Is it possible to realize Inverse Operator Method of Operator D? How to solve the following equation if we rewrite the pde through inverse operator method?

(z)(x, y)=((D[1, 1]+D[1, 2]+D[2, 2])^(-1))exp(x)*sin(y)

 

Thanks a lot.

how gr operators work?

I tried to run example given there but it is not working,

where can I get more examples to understand working of Gr operators work?

specially for raychaudhuri equations.

AOA...I want to introduce an operator to find the derivative of fractional order i.e.,

 

J^((alpha)) x^(k):=(GAMMA(k+1))/(GAMMA(k-alpha+1))x^(k-alpha):

 

when i applied J^(1/2) on x^2+x^3 it gives

 

GAMMA(3)*x^(3/2)/GAMMA(7/2)+GAMMA(4)*x^(5/2)/GAMMA(9/2)

 

Help.mw

Hello,
my question may be simple but I don't find the answer in any help guide.
when I define a function I cannot use a linearalgebra expression such as Trace.
Here is an example of what I would like to do:




If anyone can help me...
Thank you

I have a function related to some values and I want to include the value in the title.  So I initially try ...

sine:=(Amp,freq,phase,t)->Amp*sin(2*Pi*freq*t+phase):
plot(sine(1, 2, 0, t), t = 0 .. 1, title = cat(freq, " sine wave cycles"))

but once I use the value in the function it is not remembered, sort of like a subs operation.  A placeholder is the simplest way.

a:=2:
plot(sine(1, a, 0, t), t = 0 .. 1, title = cat(a, " sine wave cycles"))

Dear Maple users,

Is there a way to describe derivatives treated as binary operators in infix notation, in which the derivatives is applied either to the left or right operands. This is useful, for example, when defining generalizations of the Poisson bracket. For a pair of functions f and g, the left and right derivatives are respectively defined as

Hello,

I have created a test document to check an equation and I would like to feed a range of k values (ranging from 0 to say 512) in increments of 1) to the main function, and then plot the result as a graph of Zuncomp (y-axis) vs k(x-axis).

I can verify the values of the function by typing say Zuncomp(0) or Zuncomp(10) etc but how do you run this so that you do Zuncomp(k) to read all values of k and generate the output to plot?

Using Maple 13 (Windows 7...

here is my code i want to run the loop for every value if there is invalid input in lhs(ans(1)) the loop should not stop and check for next value
> restart;
>
> f1 := proc (x) options operator, arrow; R*T*(x*ln(x)+(1-x)*ln(1-x))+Omega[l]*x*(1-x) end proc;
x -> R T (x ln(x) + (1 - x) ln(1 - x)) + Omega[l] x (1 - x)
>
> g1 := proc (x) options operator, arrow; (1-x)*SfA*(T-TfA)+x*SfB*(T-TfB)+R*T*(x*ln(x)+(1-x)*ln(1-x))+Omega[s]*x*(1-x) end proc;

 

While substituting expressions for θ(t),θ'(t),θ''(t) with some rather simple polynoms (see attached demonstration), the result icludes terms such as "·2" or "θ1·" (see terms multiplying ε8 and ε7in result for C1). It seems MAPLE treates the "·" sign as a variable/constant instead of as an operator. What am I doing wrong?

 

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