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Schrodinger equation

  1. Mar 10, 2005 #1
    I am trying to find the Schrodinger's equation for the one-dimensional motion of an electron, not acted upon by any forces.

    So.. should I begin using the time independent form of the Schrodinger's equation? What should I arrive at? Should I let my V(x) = 0?

    Also, how do I show that the total energy of that particular schrodinger's equation is not quantized?
     
  2. jcsd
  3. Mar 10, 2005 #2

    dextercioby

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    What's the general form of the SE's equation...?What's the free particle's Hamiltonian...?

    Daniel.
     
  4. Mar 10, 2005 #3

    jtbell

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    Yes.

    Yes.

    Find the general solution of your Schrödinger equation, and show that any value of E leads to an acceptable solution for your boundary conditions. Of course, you don't really have any boundary conditions, which simplifies matters! (unlike the infinite square well a.k.a. "particle in a box" where the boundary conditions restrict the acceptable values of E to a discrete set)
     
  5. Mar 10, 2005 #4
    Thank you for your helps... I can manage from here... E = (hbar)k^2 / (2m) >= 0
     
  6. Mar 10, 2005 #5

    dextercioby

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    That's right.And the "k" wan take any real value...Making the energy spectrum the real positive semiaxis.

    Daniel.
     
  7. Mar 11, 2005 #6
    You do have boundary conditions, you have to require that your solution goes to zero at infinity, otherwise your solution is not normalizable.
    For a free particle, that actually represents a big problem, since the free particle wavefunction ([tex]e^{ipx/\hbar[/tex]) isn't nomalizable!
    That's the reason one should really work with wavepackets in the cases where [tex]V(x) = 0[/tex], those are normalizable.
    Almost any textbook in quantum mechanics has a discussion on that particular topic.
     
    Last edited: Mar 11, 2005
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