What Are the Correct Statements About a Quantum Harmonic Oscillator?

[neelakash]

Homework Statement

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.

Homework Equations

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...

 

[Gokul43201]

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.