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Wavefunction conditions

  1. May 27, 2007 #1
    hey all!
    does anyone know the conditions a well behaved wavefunction (phi) must satisfy for all x? and any physical justifications for them?

    is it something to do with continuity at boundaries? or to do with the differential of the wavefunction?

    cheers for any input

    roc
     
  2. jcsd
  3. May 27, 2007 #2

    cristo

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    In QM a well behaved function is generally a function that is continous and finite everywhere, and whose first derivative is continous and finite everywhere also.
     
  4. May 27, 2007 #3

    Doc Al

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    Try this for a start: Constraints on Wavefunction
     
  5. May 27, 2007 #4
    cheers for the help gents!
     
  6. May 27, 2007 #5
    as far as the physical justification for the constraints, are there any?
     
  7. May 27, 2007 #6
    agreed... well defined,,


    anything else?
     
    Last edited: May 27, 2007
  8. May 27, 2007 #7

    Dr Transport

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    A wave function blowing up at infinity isn't really a good thing is it????
     
  9. May 27, 2007 #8

    cristo

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    Erm... I'm not sure I know what you're getting at!
     
  10. May 28, 2007 #9
    The modulus squared of the wave function is a probability distribution. Is there any physical reason to say that at the point [tex]x = 0 + \epsilon [/tex] there's one probability density, and then at [tex]x = 0 - \epsilon[/tex] it's wildly different?

    Also, the continuous first derivative rule comes from a similar notion with regards to the momentum. I'll leave it to you to figure that one out.
     
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