SHO potential in QM

1. Nov 11, 2007

ehrenfest

1. The problem statement, all variables and given/known data
My QM book says that the standard SHO potential is $$m \omega^2 x^2/2$$. Can someone give me an example of a physical situation that is governed by this potential. It seems rather out of nowhere to me...

2. Relevant equations

3. The attempt at a solution

2. Nov 11, 2007

cristo

Staff Emeritus
Any situation that is governed by Hookes Law: f=-kx, will have a potential V=kx^2/2

3. Nov 11, 2007

ehrenfest

Yes but when is k = m \omega x? I guess \omega = g works, but
omega is usually an angle.

4. Nov 11, 2007

G01

You are probably thinking of the oscillator potential energy using the formula:

$$V=1/2kx^2$$

Remember that Omega is the angular frequency of the oscillation. Also, remember that for an oscillator obeying Hooke's Law the angular frequency is:

$$\omega = \sqrt{k/m}$$

If you solve this for k, you should see where the m*omega^2 is coming from in the book's expression for the potential energy.