Does a Quadratic Quantum Well with Given Parameters Have Three Bound States?

[smallgirl]

1. Consider a quantum well described by the potential v(x)=kx^{2}<br /> for \left|x\right|&lt;a<br /> and v(x)=ka^{2} for \left|x\right|&gt;a. Given
a^{2}\sqrt{km}/\hbar<br /> =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}<br />

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

 

[dauto]

Have you studied the solution for a harmonic oscillator yet?

 

[smallgirl]

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