1

I believe this is a simple question, however I cannot find it explained anywhere what the term:

"Impose canonical commutation relations" means.

If I have a classical equation, and I wish to quantise it, I will first promote the classical coordinates to operators, nothing more than notation change. What is the process to then impose the commutation relations for the operators that I have promoted the coordinates to?

Qmechanic
  • 220,844
Sean
  • 19

1 Answers1

1

Not sure if I understood your question totally. But when you need to change a classical entity to its quantum counterpart you need to make sure that the symmetry is observed if they are not commuting. For instance:

$xp$---change to quantum mechanical operators----> $\frac{1}{2}(\hat x\hat p+\hat p\hat x)$

or

$x^2p$---change to quantum mechanical operators----> $\frac{1}{4}(\hat x^2\hat p+2\hat x\hat p\hat x+\hat p\hat x^2)$

where $x$ and $p$ are position and momentum operators, respectively.

Amin
  • 493