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!

Infinite system of wells

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    For the (unnormalized) wave function ψ(x) = sech(ax), find the potential energy V (x), and show that the ground-state energy E1 is V(0)/2. The energies are in units of (hbar)^2a^2/2m.



    2. Relevant equations

    [tex] - \frac{\hbar}{2m}\frac{d^2 \psi}{dx^2}+V(x) \psi)=E \psi [/tex]

    3. The attempt at a solution

    I differentiated the SE twice and sub it back in to SE. Does that seem right to you?

    [tex] \frac{d^2 \psi}{dx^2} = 0.5a^2 (cosh(2ax)-3)sech^3(ax) [/tex]

    [tex] \frac{-\hbar^2}{4m} a^2 (cosh(2ax)-3)sech^2(ax)+V(x)=E=\frac{\hbar^2 a^2}{2m} [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 26, 2012 #2
    Also, I forgot to say that I got this :

    [tex] V(0)/2=\frac{3 \hbar^2 a^2}{8m} [/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Infinite system of wells
  1. Infinite square well (Replies: 5)

Loading...