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Question: How to improve physics Simplify for an Angular Momentum problem

Question:How to improve physics Simplify for an Angular Momentum problem

otaviosama 5 Maple 18
simplify physics
October 21 2019
1

Hello,

I'm trying to verify a computation using maple. But the simplification of Physics doesn't return the right value.

The computation is

I wrote the follow code


 

> 

> 

J[x]^2*J[z]^2+(J[x]*J[z]*J[x])*J[z]+J[x]*J[z]^2*J[x]+J[x]^2*J[z]*J[z]+(J[x]*J[z]*J[z])*J[x]+J[x]^2*J[z]^2 = 3*J[x]^2*J[z]^2+3*J[x]^2*J[z]^2+2*J[x]^2-3*J[y]^2+2*J[z]^2

``

> 

restart; with(Physics)*Setup(noncommutativepre = J)
> 

CommuRules := seq(op([%Commutator(J[j[1]], J[j[2]]) = I*J[j[3]]]), j = [[x, y, z], [y, z, x], [z, x, y]])
> 

NULL
> 

NULL
> 

Setup(CommuRules)

[algebrarules = {%Commutator(J[x], J[y]) = I*J[z], %Commutator(J[y], J[z]) = I*J[x], %Commutator(J[z], J[x]) = I*J[y]}]

 (1)
> 

NULL
> 

with(combinat)
> 

np := numbperm([J[x], J[x], J[z], J[z]], 4)

6

 (2)
> 

> 

``
> 

``
> 

L := permute([J[x], J[x], J[z], J[z]], 4)

[[J[x], J[x], J[z], J[z]], [J[x], J[z], J[x], J[z]], [J[x], J[z], J[z], J[x]], [J[z], J[x], J[x], J[z]], [J[z], J[x], J[z], J[x]], [J[z], J[z], J[x], J[x]]]

 (3)
> 

``
> 

NULL
> 

L2 := seq(map(proc (x, y, z, t) options operator, arrow; x*y*z*t end proc, op(L[i])), i = 1 .. np)

Physics:-`*`(Physics:-`^`(J[x], 2), Physics:-`^`(J[z], 2)), Physics:-`*`(J[x], J[z], J[x], J[z]), Physics:-`*`(J[x], Physics:-`^`(J[z], 2), J[x]), Physics:-`*`(J[z], Physics:-`^`(J[x], 2), J[z]), Physics:-`*`(J[z], J[x], J[z], J[x]), Physics:-`*`(Physics:-`^`(J[z], 2), Physics:-`^`(J[x], 2))

 (4)
> 

S := add(j, j = L2)

Physics:-`*`(Physics:-`^`(J[x], 2), Physics:-`^`(J[z], 2))+Physics:-`*`(J[x], J[z], J[x], J[z])+Physics:-`*`(J[x], Physics:-`^`(J[z], 2), J[x])+Physics:-`*`(J[z], Physics:-`^`(J[x], 2), J[z])+Physics:-`*`(J[z], J[x], J[z], J[x])+Physics:-`*`(Physics:-`^`(J[z], 2), Physics:-`^`(J[x], 2))

 (5)
> 

NULL
> 

NULL
> 

S1 := Simplify(S, algebrarules)

-(3*I)*Physics:-`*`(J[x], J[y], J[z])-7*Physics:-`^`(J[z], 2)-(8*I)*Physics:-`*`(J[z], J[x], J[y])+6*Physics:-`*`(Physics:-`^`(J[z], 2), Physics:-`^`(J[x], 2))-I*Physics:-`*`(J[y], J[z], J[x])

 (6)
> 

NULL
> 

NULL

``


 

Download MapleCode.mw

 


If someone knows, or have suggestions that what i can do to find the right result, plz let me know
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