(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of mass m and energy E<V_{0}is trapped in the 1-D potential well defined by,

V=[tex]\infty[/tex], x<0; V=0, 0[tex]\leq[/tex]x[tex]\leq[/tex]L; V=V_{0}, x>L.

(b) Obtain solutions to the time independent schrodinger equation for the three regions and by appropriate matching at the boundaries, show that the allowed energies are given by the transcendental equation, [tex]k cot(kL)=-\kappa[/tex], [tex]where[/tex][tex] {k^2}=\frac{2mE}{\hbar^2},{\kappa^2}=\frac{2m({V_0}-E)}{\hbar^2}[/tex].

2. Relevant equations

TISE

3. The attempt at a solution

For region 2,

[tex]\frac{{\partial^2}\psi}{\partial{x^2}}+\left(\frac{2mE}{\hbar^2}\right)\psi=0[/tex]

[tex]\frac{{\partial^2}\psi}{\partial{x^2}}+{k^2}\psi=0[/tex]

[tex]\psi(x)=Asin(kx)+Bcos(kx)[/tex]

I don't understand how to get from line two to line 3, and where does the potential term disappear to?

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# Homework Help: 1-D potential TISE

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