MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Quantum Commutator

Dear Dick, 
I'm sorry this is sort of late in the post, but I just came across your query looking for similar software using Google.   As it turns out, a bit of
digging through my own quantum mechanics course notes yields a nice solution. 

There's a nice relation you my wish to exploit in calculating quantum commutators. I believe it's originally due to Dirac.   
In essence, if you have quantum operators A(p,q) and B(p,q)  as functions of the quantum p & q operators, then 
[A,B] = i hbar {A,B}
where {A,B} is the classical poisson bracket.  This is easy to code in Mathematica! In addition you can generalize this to any set of 
canonical variables, for example the boson operators a & a^\dagger.
For example, if you have operators A(a,a^\dagger) and B(a,a^\dagger)
[A(a,a^\dagger), B(a,a^\dagger)] = i hbar (\partial_a A \partial_{a^\dagger}B-
\partial_{a^\dagger}A\partial_a B
For fermions, you need to modifiy this to take in to account Pauli exclusion,  but that's simple since you can relate the commutator to the 

Eric B.

  • Prev by Date: Re: RE: Fourier Series Expansions and it's Coefficients question revised tia
  • Next by Date: Re: How should I start with mathematica?
  • Previous by thread: Re: Tooltips and PlotMarkers
  • Next by thread: Weights in NonlinearRegress / NonlinearFit. Versus data errors