Quantum harmonic potential problem

[theWapiti]

Homework Statement

Consider a particle of mass m in a harmonic potential:

If the particle is in the first excited state (n = 1), what is the probability of finding the
particle in the classically excluded region?

Homework Equations

The Attempt at a Solution

I sub in

and get a wave function:

But I don't know how to set my bounds for the normalization integral.

I've been advised that the classical limits are:

But I'm still stuck.

 

[Oxvillian]

theWapiti - the classically excluded region is where the potential $V(x)$ exceeds the total energy of the system, which in this case is $\frac{3}{2}\hbar\omega$. You need to find out how much of your wavefunction lies in this region. The integral given will probably come in useful for doing that.

[I suggest the powers that be move this thread to "Advanced Physics Homework"]