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Bound states.

  1. Dec 13, 2014 #1
    1. The problem statement, all variables and given/known data
    A particle is in the following potential:
    V(x)=infinity for x<0; -V0 for 0<x<a; and 0 for x>a
    Given that there's only one bound state I am asked to determine the range of values for V0 in terms of the width a and the particle's mass m.



    2. Relevant equations


    3. The attempt at a solution
    For -V0<E<0 I chose the following general solution for the wave function:
    ψ(x)=Asin(kx) 0<x<a; Bexp(-qx) x>0
    where k=√(2m(E+V0)/ħ and q=√(2m|E|)/ħ
    By demanding continuity at x=a for both wave functions and their derivatives I obtained the following solution:
    q=-kctg(ka)
    How may I proceed? I'd appreciate some guidance.
     
  2. jcsd
  3. Dec 14, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    How do you get the number of solutions from your last equation?
    The borders for "a" and "m" are exactly the limiting cases for 1 and 2 solutions.
     
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