Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

Question:
Consider a particle with energy E bound to a finite square well of height U and width 2L situated on -L<x<+L. Because the potential energy is symmetric about the midpoint of the well, the stationary state waves will be either symmetric or antisymmetric about this point. (a) Show that for E<U, the conditions for smooth joining of the interior and exterior waves lead to the following equation for the allowed energies of the symmetric waves:
k tan (kL) = \alpha
where \alpha = \sqrt{(2m/(h-bar)^{2})(U-E)}
and k = \sqrt{2mE/(h-bar)^{2}}
is the wavenumber of oscillation in the interior.

My Problem:
I don't think I fully understand the question. I can see that 1/\alpha is the penetration depth, but I am unsure where the rest of the equation comes from, and not fully understanding the theory behind it doesn't help. I've read through the related part of my book twice, and looked in other books, but there's obviously something I'm missing.

And I didn't put in part (b) as it's basically more of the same thing, so I figure once I figure out part (a), part (b) will be easier.

Thank you for any help