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Schroedinger Equation Questions

  1. Aug 4, 2011 #1
    Hi! Im having some problems in setting up the Schrodinger equation for a particle described by the wave function:

    [itex]\Psi[/itex] = A sinh (x)

    should I use the exponential form of the hyperbolic function?

    [URL]http://62.0.5.135/upload.wikimedia.org/math/9/c/7/9c74b71126c6bb1f4d6b865019a2735e.png[/URL]


    Also, for normalization, do you have any guides that show how to form the complex conjugate of the above function (i dont see the complex parts).
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Aug 4, 2011 #2
    What's the problem with the Schroedinger equation? Are you using the time-independent version (I assume you should be), is there a potential energy associated with this wavefunction?

    Further, the complex conjugate of a real valued function is just the real function again. So normalization should look something like:

    1=A2 [itex]\int[/itex]sinh2(x)dx
     
    Last edited: Aug 4, 2011
  4. Aug 4, 2011 #3
    This is my solution to the normalization of the wave equation. Im sorry im totally new at this.

    [PLAIN]https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc6/249293_246586558696823_100000364410765_866703_7618168_n.jpg [Broken]

    Is it correct? I just followed wikipedia's
    http://en.wikipedia.org/wiki/Normalizable_wave_function#Example_of_normalization

    My question on the Schroedinger Eq. is that: Should i use the exponential form of the hyperbolic function? or does it matter if i use the hyperbolic? In the normalization above i used the exponential form.
     
    Last edited by a moderator: May 5, 2017
  5. Aug 4, 2011 #4
    When you use the wavefunction in the Schrodinger equation, it shouldn't matter what form (hyperbolic or exponential) you use. Your normalization is off however. The integral of sinh2(x) is:

    Exponential form: [itex]\frac{1}{4}[/itex] (exp(2x)/2+exp(-2x)/2-2x)
    Hyperbolic form: [itex]\frac{1}{4}[/itex] (sinh(2x) -2x)

    Further, you need to take the integral only between o and L, the other parts can be ignored. I may be reading this wrong, but it seems like you tried to absorb the exponentials into A2 and ignored any actual integration.

    Cheers,
    -Malus
     
  6. Aug 4, 2011 #5
    thanks! I did the integration. and found what the factor is. thanks also for pointing that hyperbolic or exponentials can be used!.
     
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