2k views

### What physical significance has the Heisenberg Group?

I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, ...
2k views

### Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
113 views

### Eigenvectors and Eigenvalues of $a^\dagger a$ [duplicate]

A common question I have seen on problems sets and on exam papers is as follows (own words): Show that $a^\dagger$ and $a$ satisfy the canonical commutation relations. Hence show write down the ...
119 views

### Analysis of Harmonic Oscillator [duplicate]

In griffiths, Why was the lowest chosen like that while in the ladder analogy, the lower energies are like $a_-^n\psi$? That is, why didnt he chose the lowest rung to be $$a_-^n\psi$$
76 views

### Proportionality of states in quantum harmonic oscillator

What is the justification for $a_{\pm} \psi_{n}$ being proportional to $\psi_{n\pm1}$ in a quantum harmonic oscillator? Here $a_{\pm}$ is the raising/lowering ladder operator.
389 views