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Forums
Physics
Quantum Physics
Finite square well bound states
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[QUOTE="andrewtz98, post: 6011161, member: 646946"] Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with: $$ \tan(k_1a)=-\frac{k_1}{k_2},$$ where ##k_1=\sqrt{\frac{2mE}{\hbar^2}}## and ##k_2=\sqrt{\frac{2m(V_o-E)}{\hbar^2}}##. I'm aware of the fact that solutions can only be calculated graphically, but what's the relation between the value of ##V_o## and the bound states? What if I want to find the acceptable values of ##V_o## for the bound states to be ##1,2,3,\dots## or none? [/QUOTE]
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Quantum Physics
Finite square well bound states
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