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

[smallgirl]

1. Consider a quantum well described by the potential $$v(x)=kx^{2}$$ for $$\left|x\right|<a$$ and $$v(x)=ka^{2}$$ for $$\left|x\right|>a$$. 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 $$\intop(1-y^{2})^{1/2}dy=\frac{\pi}{2}$$

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...