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messedmonk18
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Possible bound states of a one-dimensional square well... I'm Lost!
Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4?
p=ka/2 & p(max)^2 = (u(not)a^{2}/4), u(not) = \underline{2m(not)}\overline{\hbar^{2}}V(not)
I've found that for Even parity: p tan(p)= \sqrt{p(max)^{2}-p^{2}}
Odd: -p cot(p)= \sqrt{p(max)^{2}-p^{2}}
So after I've found the Even and Odd solutions from a lot of algebra I'm completely lost on how to find the number of bound states. I assume that this has to do with integers of k but I'm not sure what this all means and how to derive a "bound" state from the information given. I need a lot of help... or at least some just to get started!
Homework Statement
Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4?
Homework Equations
p=ka/2 & p(max)^2 = (u(not)a^{2}/4), u(not) = \underline{2m(not)}\overline{\hbar^{2}}V(not)
I've found that for Even parity: p tan(p)= \sqrt{p(max)^{2}-p^{2}}
Odd: -p cot(p)= \sqrt{p(max)^{2}-p^{2}}
The Attempt at a Solution
So after I've found the Even and Odd solutions from a lot of algebra I'm completely lost on how to find the number of bound states. I assume that this has to do with integers of k but I'm not sure what this all means and how to derive a "bound" state from the information given. I need a lot of help... or at least some just to get started!