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Forgoten a vital part in QM

  1. May 22, 2007 #1
    In Quantum Mechanics the one of the constraints on the wavefunction is that its derivative is continuous, what I have a problem with is that I have forgotten what this actually means in terms of an equation.

    ie

    [tex] \frac{d\psi){dx}=?[\tex]

    This is driving me nutty and looked on the internet but not found what I am looking for! If some one can help me then that would be great!!

    Thank you

    newo
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: May 22, 2007
  2. jcsd
  3. May 22, 2007 #2

    malawi_glenn

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    Suppose we have this potential shape:

    a, V = +inf at x < 0
    b, V = - V_0 at 0 < x < a V_0 > 0
    c, V = 0 at x > a

    We get one wavefuntion at region b, call it psi_1(x) and one for region c, called psi_2(x), by solving the shrödinger equation.

    Now psi_1(a) = psi_2(a)
    and
    d(psi_1(a))/dx = d(psi_2(a))/dx

    and we have:

    psi_1(a) / [d(psi_1(a))/dx ] = psi_2(a) / [d(psi_2(a))/dx]

    was it this you were looking for?
     
  4. May 22, 2007 #3
    Thats what i was looking for i remember now thanks!

     
  5. May 22, 2007 #4

    malawi_glenn

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    hehe great, Good luck with the QM! =)

    You can also check with the definitions and requriments of an continous function in calcus books.
     
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