# Harmonic Oscillator problem

1. Dec 3, 2007

### neelakash

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

For a 1D QM harmonic oscillator,

(a) the discrete energy states are nhw

(b) the discrete energy states are (n+0.5)hw

(c) the lowest energy state wave function is ~$$\exp^\frac{-\alpha^2\ x^2}{2}$$

(d) the probabilty of finding the particle outside the classical limit is non-zero.

2. Relevant equations

3. The attempt at a solution

I think (b) and (c) are correct...by theory...

Should not (d) be also correct?--outside the classical limit=>inside quantum domain...

Last edited: Dec 3, 2007
2. Dec 3, 2007

### Gokul43201

Staff Emeritus
Yes, d is also correct. It is useful to do the calculation (one time in your life; and the sooner the better) to estimate the probability of finding the particle in its ground state outside the classical turning points.