(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] QM simple harmonic oscillator

1. The problem statement, all variables and given/known data

If I have a particle in an SHO potential and an electric field, I can represent its potential as:

[tex] V(x) = 0.5 * m \omega^2 (x - \frac{qE}{mw^2})^2 - \frac{1}{2m}(\frac{qE}{\omega})^2 [/tex]

I know the solutions to the TISE:

[tex] -\hbar^2 /2m \frac{d^2 \psi}{ dx^2} + 0.5 m\omege^2 x^2\psi(x) = E\psi(x) [/tex] (*)

(Those are different Es)

So, I plug V(x) into the TISE and get:

[tex] -\hbar^2 /2m \frac{d^2 \psi}{ dx^2} + (0.5 * m \omega^2 (x - \frac{qE}{mw^2})^2 - \frac{1}{2m}(\frac{qE}{\omega})^2) \psi(x) = E\psi(x) [/tex]

Now, since we only shift and translated the potential, I should be able to find a substitution for x that yields the equation (*) in a new variable y = f(x), right?

The problem is, after I move the constant term to the RHS, I cannot find the right substitution. What am I doing wrong?

2. Relevant equations

3. The attempt at a solution

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

Dismiss Notice

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: QM simple harmonic oscillator

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