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Quantum mechanics

  1. Nov 4, 2005 #1
    if you know the wave ...
    how do you determine the reflected and transmitted waves?

    the book tells you to enforce the required continuity conditions to obtain their (possibly complex) amplitudes
  2. jcsd
  3. Nov 4, 2005 #2


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    You cannot expect a coherent answer when you ask something this vague.

  4. Nov 4, 2005 #3
    As vague as that question is, I think the answer you are looking for is that:

    Y= Psi because I dont know how the nifty regulars use that fancy font
    Yi: Incident wave
    Yr: Reflected wave
    Yt: Transmitted wave
    Y': Derivative of wave equations with respect to position (x)

    Lets assume that the potential barrier is at x = a
    you have two continuity equations

    Yi(a) + Yr(a) = Yt(a)
    Yi'(a) + Yr'(a) = Yt'(a)

    I doubt that answers your question since im not sure what it is, but you can figure everything out from these continuity equations.
  5. Nov 4, 2005 #4
    Let me type the exact q ...

    A beam of particles of energy E and incident upon a potential step of U0 = 3/4 E is described bby the wae funciton
    Y(x) = 1 e^(ikx)
    The amplitude of the wave (related to the number incident per unit distance) is arbitrarily chosen as unity.
    a) Determine completely the reflected and transmitted waves by enforcing the required continuity conditions to obtain their (possibly comlex) amplitudes
    b) Verify that the ratio of reflected probability desnity to the incident probability desnity agrees with
    the equation ... T = .... R = ....

    what i dont get is what the hell is "required continuity conditions"
  6. Nov 4, 2005 #5
    The wavefunction and it's derivative must be continuous at the barrier's edge.
  7. Nov 4, 2005 #6


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    ...which is a specific part of the requirement that the wavefunction be continuously derivable EVERYWHERE.
  8. Nov 4, 2005 #7


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    You can use Latex, or go here from where you can copy and paste individual characters.
  9. Nov 5, 2005 #8


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    wave function derivatives

    Gokul, with step functions, delta-functions, and linear-cusp functions being commonplace portions of model potentials, that was a VERY misleading thing to say.:yuck:
    If the Potential is smooth, then the wave function will be also;
    If the Potential has infinities, jumps, or kinks, then the wave function
    will have discontinuous 1st, 2nd, or 3rd derivitives ...
    otherwise the equation isn't satisfied.
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