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: Potential wells

  1. May 2, 2008 #1
    1. The problem statement, all variables and given/known data
    A potential well with V(x)=0 for x<0 and V(x) = Vo for x>0. The particle has energy E greater than Vo and is incident from the left side. Calculate the reflection coefficient.

    2. Relevant equations

    Relfection coefficient is given by R= (B*B)/(A*A)

    3. The attempt at a solution
    I think that the time independent Schrodinger equation for the two regions are
    x<0 (-hbar/2m)dphisquared/dphi =Ephi(x)
    x>0 ((-hbar/2m)dphisquared/dphi +Vo phi = Ephi(x)

    the solutions to this
    x<0 Aexp(ik1x) +Bexp(-ik1x) = phi(x)
    x>0 Cexp(ik2x)

    is this right
    carrying this through and equating two solutions at x=0
    A+b = C
    and equating differentials at x=0 gives
    ik1(A-B) = -ik2C/k1

    but when I solve for A and B i get

    when I find R i get R=1 which must wrong because particle is not always reflected it should pass over the potential barrier?
  2. jcsd
  3. May 2, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Things started to break down when you evaluated the derivatives. Why is there a k1 on the left side? And why didn't the i's cancel out in the final solution?
  4. May 3, 2008 #3


    User Avatar
    Homework Helper
    Gold Member

    Apart from the extra k1 on the left side which Dick pointed out, why is there a minus sign on the right side?
  5. May 3, 2008 #4
    sorry should the differentials be (A-B)=-ik2C/k1?
    in which case i still get the same solutions for A and B and a coefficient of 1
  6. May 3, 2008 #5


    User Avatar
    Homework Helper
    Gold Member

    Why is there a minus sign on the left hand side?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook