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General solution of the Schrodinger equation for a free particle?

  1. Jun 28, 2014 #1
    1. The problem statement, all variables and given/known data
    I'm trying to figure out how the general solution of the Schrodinger equation for a free particle when v=0 relates to anything I have learned in class...


    2. Relevant equations
    For Eψ=(hbar2/2m)d2ψ/dx2


    3. The attempt at a solution
    I really have no idea- what is confusing me is that ψ is a function rather than a constant so I don't know how to treat it...

    Thank you all for any help!

    And I really apologise for the equation... I don't really understand how to use LaTeX
     
  2. jcsd
  3. Jun 28, 2014 #2

    ehild

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    You miss the negative the sign: ##-\hbar^2/(2m)d^2ψ/dx^2=Eψ##

    That is a differential equation of form y"+kx=0. What is the solution?

    The former equation is the time independent equation for one dimension. The time dependent equation is

    ##i\hbar \frac{\partial ψ}{\partial t}=-\hbar^2/(2m)\frac{\partial^2}{\partial x^2}##

    ehild
     
    Last edited: Jun 28, 2014
  4. Jun 28, 2014 #3

    haruspex

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    y"+ky=0?
     
  5. Jun 28, 2014 #4

    ehild

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    I meant it so. Thanks.

    ehild
     
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