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: Reflection Coeff - Quantum Mech

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the reflection coefficient for electrons traveling toward a potential change from [tex]V[/tex] to [tex]V_0[/tex] with a total energy [tex]E > V_0[/tex].
    The potential diagram is just a unit step function. It goes from [tex]V = 0[/tex] to [tex]V = V_0[/tex] at [tex]x=0[/tex]. In piecewise notation:
    V(x) = \left\{
    0 & : x < 0 \\
    V_0 & : x \ge 0
    The piecewise notation does not account for the [tex]V(x)[/tex] being continuous at [tex]x=0[/tex].

    2. Relevant equations
    a) Probability flux:
    [tex]S\left( x,t \right)=-\frac{i\hbar}{2m}\left[ \Psi^*\left( x,t \right) \frac{\partial \Psi\left( x,t \right)}{\partial x} - \Psi\left( x,t \right) \frac{\partial \Psi^*\left( x,t \right)}{\partial x}\left][/tex]

    b) Reflection coefficient:
    [tex]R=\frac{S_{I}^{-x}\left( x,t \right)}{S_{I}^{+x}\left( x,t \right)}[/tex]

    3. The attempt at a solution
    I've solved for the wave equations at [tex]x > 0[/tex] and [tex]x < 0[/tex]. I'm stuck as far as where to go from there.
  2. jcsd
  3. Apr 8, 2010 #2
    Are you asking for help on (a)? Can you also show us your final wave function? And have you tried plugging that wavefunction into (a)?
  4. Apr 8, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Require continuity of the wavefunction and its derivative at x=0. That will allow you to solve for most of the constants.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook