1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finite Square Well Problem

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Based on the finite potential well defined by the following equations, how many bound states are there, which of these states are even and which are odd, and what are their energies?


    V(x)= 0 for x[tex]\leq[/tex]-l/2 and x [tex]\geq[/tex] +l/2
    V(x)=-[tex]\hbar[/tex][tex]^{2}[/tex]/ma[tex]^{2}[/tex]



    2. Relevant equations

    E=n[tex]^{2}[/tex][tex]\hbar[/tex][tex]^{2}[/tex]/2mL[tex]^{2}[/tex]


    3. The attempt at a solution

    To find the number of states I set [tex]\hbar[/tex][tex]^{2}[/tex]/ma[tex]^{2}[/tex] equal to E=n[tex]^{2}[/tex][tex]\hbar[/tex][tex]^{2}[/tex]/2mL[tex]^{2}[/tex], substituting the value l in for L to get n[tex]\leq[/tex]8[tex]^{1/2}[/tex]

    So this tells me that there are 2 bound states. N = 1 is the odd function, and N=2 is the even function. I do not however know how to get their energies, nor do I know if this is the correct way to solve the problem. Do I need to define the hamiltonian in the problem? If so, how do I go about doing that?
     
  2. jcsd
  3. Oct 16, 2008 #2
    I am afraid your formula for energy is valid only for an infinite well.
    Here you have a finite well (with "depth" = h^2/ma^2).
    You have to solve Schrodinger equation for the three zones (x<-1/2, x between -1/ and 1/2 and x>1/2) and then impose boundary conditions. The wave functions from the neighboring regions must match at the boundary. These conditions will provide the allowed energies.
    You may need to solve the "matching" equation numerically.
    Good luck!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Finite Square Well Problem
Loading...