1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Double delta-function potential

  1. Oct 22, 2011 #1
    My session expired while typing this post, so this is my second attempt at typing it. I *always* forget to paste into notepad before submitting these darned things.
    1. The problem statement, all variables and given/known data

    Problem 2.27, Griffiths.

    Given two delta potential wells at +a and -a, determine the number of bound states, find their associated energies, sketch the wave functions.

    2. Relevant equations

    [itex]V(x) = -\alpha\left[\delta\left(x+a\right)+\delta\left(x-a\right)\right][/itex]

    3. The attempt at a solution

    This is the first problem in the book where I really do not know where to begin. I know that the answer has to be in some form of exp(kt) where k is sqrt(-2*m*E)\hbar.

    I vaguely understand the book's process for the logic behind constructing the wave function for a single delta potential well, but clearly not well enough.
  2. jcsd
  3. Oct 22, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Start by solving the Schrodinger equation in the three regions x<-a, -a≤x≤a, and x>a.
  4. Oct 22, 2011 #3
    Thanks for the assistance. All I had to do was solve for a 0 potential and pay attention to the boundary conditions (continuous function, discontinuous derivative by a specific value).

    The hard part, after that, was not getting lost in the algebra. I still don't quite understand how to solve for the energy, though. I ended up with two equations that needed numerical solving, one for the even wave function, and one for the odd wave function.

    Overall, this problem was a real curve ball, and the specific questions this problem asked were far more confusing to me than any of the others.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook