(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is A in [itex]\bar{\varphi}[/itex]A[itex]\varphi[/itex], if

[itex]\bar{\varphi}[/itex]A[itex]\varphi[/itex] = [itex]\frac{-ip(\tau)\dot{q}(\tau)}{\hbar}[/itex]+[itex]\frac{p^{2}(\tau)}{2m}[/itex]+[itex]\frac{m\omega^{2}}{2}[/itex]q[itex]^{2}[/itex]([itex]\tau[/itex])

2. Relevant equations

provided that [itex]\bar{\varphi}[/itex] and [itex]\varphi[/itex] are ladder operators of the form:

[itex]\varphi[/itex] = [itex]\left(\frac{m\omega}{2\hbar}\right)^{1/2}[/itex][itex]\left(q\left(\tau\right)+\frac{ip\left(\tau\right)}{m\omega}\right)[/itex]

[itex]\bar{\varphi}[/itex] = [itex]\left(\frac{m\omega}{2\hbar}\right)^{1/2}[/itex][itex]\left(q\left(\tau\right)-\frac{ip\left(\tau\right)}{m\omega}\right)[/itex]

p is the momentum and q is the position in real space,

3. The attempt at a solution

A possible solution might be to extract all those variable to get A, but [itex]\bar{\varphi}[/itex] and [itex]\varphi[/itex] are operators, so i am in complete darkness here, i hope you have a possible solution to this, thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Harmonic osccillator: solution for A in Y'AY

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**