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Question: QM perturbation theory: too many levels of recursion

Question:QM perturbation theory: too many levels of recursion

w-Teilchen 80 Maple 18
physics recursion perturbation
October 09 2014
2

Hello everyone,

I've been trying to do some perturbation theory and ran into some problems I don't quite understand. I implemented the Hamiltonian of the Bose-Hubbard model and treated the hopping as a perturbation. Calculating the second order energy shift is easily accomplished, but when I'm only interested in one of the two occuring terms, I run into problems. The calculation takes minutes to finally fail, giving me an "too many levels of recursion"-error. I need to be able to just pick a few terms for some calculations, I'm doing, and can't figure out what I might be doing wrong. Here is the source code (download is below):

> 

restart; with(Physics); Setup(mathematicalnotation = true)
> 

a__1 := Annihilation(N, 1):
> 

assume(`and`(`in`(m, nonnegint), m > 0)):

Physics:-Ket(N, m, m)

 (1)
> 

H := Physics:-`*`(Physics:-`*`(1/2, n__1), n__1-1)+Physics:-`*`(Physics:-`*`(1/2, n__2), n__2-1):
> 

`ΔE__2` := Physics:-`*`(Physics:-`*`(2, d), simplify(value(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Dagger(psi), V), 1/(E(m, m)-H)), V), psi))))

-4*d*J^2*m*(m+1)

 (2)
> 

simplify(value(((Dagger(psi).c__2)*a__1.(1/(E(m, m)-H)).c__1)*a__2.psi))

Error, (in PatternMatching:-AlgStruct:-Match) too many levels of recursion

  
> 

``

Download too_many_levels_of_recursion.mw

It would be great, if someone could point out the mistake, I'm making. I copy/pasted the last line, so there shouldn't be any typos.

Thanks in advance,

Sören
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