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

V(x) = [tex]\left\{\infty \textrm{ for } x<0[/tex]

[tex]\left\{0 \textrm{ for } 0<x<a[/tex]

[tex]\left\{V_0 \textrm{ for } a<x<a+2b[/tex]

[tex]\left\{0 \textrm{ for } a+2bx<2a+2b[/tex]

[tex]\left\{\infty \textrm{ for } 2a+2b<x[/tex]

Set up the relevant equations in each region, write down the appropriate solution and then show that the wavenumber of the wave functions inside and outside the barrier satisfy a transcendental equation.

2. Relevant equations

3. The attempt at a solution

I have basically used Schrödinger equations for the energy for regions 1 2 and 3. but this is where i get stuck. I have to show the energies that work (hope that makes sense). I'm not suppose to solve for [tex]E>V_0, E=V_0 or E<V_0[/tex] but find the energies that work. I am a bit confused about the boundary conditions also. I set them up the same as a finite potential barrier, but do i need boundary conditions for x<0 and x>2a+2b? as these sections are infinite, we should just get 100% reflection?

I am also confused about the barrier in the middle. When solving for [tex]E>V_0, E=V_0 or E<V_0[/tex] we have different Schrödinger equations and different boundary conditions. How do i do it for any value of E?

I guess you all know by now i am pretty stuck lol.

Hope someone can help =)

and hope my LaTeX and writing is easy to understand =P

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# Homework Help: Double Potential Well

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