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Question: Substituting for expressions that contain operators from the Physics package

Question:Substituting for expressions that contain operators from the Physics package

itsme 769 Maple
substitution subs algsubs physics
October 26 2021
3

What's the simplest way to partially substitute for expressions that contain operators from the Physics package? 
(hopefully my worksheet below shows what I mean)
Thanks

> 

restart:
> 

with(Physics):
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1092 and is the same as the version installed in this computer, created 2021, October 18, 14:11 hours Pacific Time.`

 (1)
> 

Setup(quantumoperators = {sigma__x, sigma__y, sigma__z, rho, H, comm}, mathematicalnotation = true);

[mathematicalnotation = true, quantumoperators = {H, comm, rho, sigma__x, sigma__y, sigma__z}]

 (2)

we could just use Physics:-Psigma, etc... but here let's define these manually:

> 

Setup(algebrarules={
%Commutator(sigma__x, sigma__y) = 2*I*sigma__z,
%Commutator(sigma__y, sigma__z) = 2*I*sigma__x,
%Commutator(sigma__z, sigma__x) = 2*I*sigma__y
}
);

[algebrarules = {%Commutator(sigma__x, sigma__y) = (2*I)*sigma__z, %Commutator(sigma__y, sigma__z) = (2*I)*sigma__x, %Commutator(sigma__z, sigma__x) = (2*I)*sigma__y}]

 (3)

some expression (normally long and complicated that contains many operators):

> 

expr:=(sigma__y*sigma__x*rho - sigma__y*rho*sigma__x);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

 (4)

say want to make this type of substitution:

> 

subs_vars:=sigma__y*sigma__x=H;

Physics:-`*`(sigma__y, sigma__x) = H

 (5)

this doesn't work

> 

algsubs(subs_vars, expr);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

 (6)

this also doesn't work:

> 

subs(subs_vars, expr);

Physics:-`*`(sigma__y, sigma__x, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

 (7)

this works (here we explicitly specify the whole thing, that includes rho)

> 

subs(sigma__y*sigma__x*rho=H*rho, expr);

Physics:-`*`(H, rho)-Physics:-`*`(sigma__y, rho, sigma__x)

 (8)

but I would like for the substitution to also work for *parts* of the expression, as in the normal case, when not using operators.

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