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Normalization constant

  1. Mar 6, 2005 #1
    How do I calculate the normalization constant for a wavefunction of the form (r/a)e^(-r/2a) sin(theta)e^(i*phi)?

    How would I write the explict harmonic oscillator wavefunction for quantum number 8(in terms on pi, alpha, and y)

  2. jcsd
  3. Mar 6, 2005 #2
    Remember that the probability of the particle existing somewhere in all space is certain. So we have


    For the case of the wavefunction you have been given, an exact anti-derivative exists with these particular limits.

    EDIT: Now correct for the 1D case. See jtbell's post for the correct answer.
    Last edited: Mar 7, 2005
  4. Mar 6, 2005 #3


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    No, this is a three-dimensional wave function in spherical coordinates, so the integral looks like this:

    [tex]\int_0^{2 \pi} {\int_0^{\pi} {\int_0^{\infty}{\psi^*(r, \theta, \phi) \psi(r, \theta, \phi)} r^2 \sin \theta \ dr} \ d\theta} \ d\phi} = 1[/tex]
  5. Mar 7, 2005 #4
    Yes, of course, jtbell is correct. Sorry. What I wrote was wrong even in the 1D case.
  6. Mar 7, 2005 #5


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    It was correct in the ID case,those wave functions are scalars (bosonic variables) and can be switched places inside the integral.

  7. Mar 7, 2005 #6


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    How many dimensions does this oscillator have...?It's essential to know this fact.As for the variables you posted,they couldn't ring a bell,because notation conventions are not unique... :wink:

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