# Homework Help: Quantum Wells: WKB approximation

1. Mar 26, 2014

### smallgirl

1. Consider a quantum well described by the potential $$v(x)=kx^{2}$$ for $$\left|x\right|<a$$ and $$v(x)=ka^{2}$$ for $$\left|x\right|>a$$. Given
$$a^{2}\sqrt{km}/\hbar =2$$, show that the well has 3 bound states and calculate the ratios between the energies and $$ka^{2}$$.
You may use the standard integral $$\intop(1-y^{2})^{1/2}dy=\frac{\pi}{2}$$

I am not sure how to begin the question, really stuck.... Would love some help to get me started.

2. Mar 26, 2014

### dauto

Have you studied the solution for a harmonic oscillator yet?

3. Mar 26, 2014

### smallgirl

No but I know I'm not meant to do it like that....