I have a particle in a spherical well with the conditions that V(r) = 0 is r < a, and V(r) = V(adsbygoogle = window.adsbygoogle || []).push({}); _{0}if r ≥ a.

In this problem we are only considering the l=0 in the radial equation.

After solving this I found that in the region 0<r<a, u(r)=Bsin(kr) (k=√2mE/hbar), and in the other region, u(r)=Bexp(-la) (l=√2m(E+V_{0}/hbar). I was supposed to show that in order to find E I needed to solve a transcendental equation of the form sinθ=±ςθ, however my result was l=ktan(ka), so I am unsure what to do with this.

Also, I was wondering why is it that there is a possibility of there being no bound states if V_{0}is too small? And how would I go about finding this minimum potential?

Thanks!

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