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Question about Dirac form

  1. May 11, 2008 #1
    I am studying for a Quantum Mechanics final and our prof. gave us an equations sheet with some of the equations needed for the exam.
    I was wondering what the following equations could be used for. We have covered spherical harmonics, the Hydrogen Atom, Degenerate Perturbation Theory, Spin, Stationary Electron in a Magnetic field, Addition of Angular Momentum (J, Jz) using Clebsch Gordon table, and Spin Orbit and the Zeeman Effect. I am a little confused by the dirac form.

    Sorry about the pdf form... it wouldnt let me paste the code into the text!


    Attached Files:

  2. jcsd
  3. May 11, 2008 #2
    What he has written down is in fact [tex]\left\langle \mathbf{r} | 0 1 \right\rangle[/tex]
    Presumably, you could use these equations to find, say, [tex]\left\langle y^2 \right\rangle[/tex] for the 2D harmonic oscillator.
  4. May 12, 2008 #3
    I am not familiar with that form... is that just Psi(r)? and what quantum numbers are the 0 and 1?
    Thanks again!
    Last edited: May 12, 2008
  5. May 12, 2008 #4
    Mmm... it would be a good idea for you to review Bra/ket notation. The state in this case is one of the excited states of the quantum harmonic oscillator:

    [tex]\left| n_x = 0, n_y = 1\right\rangle[/tex].

    I'm talking about the overlap of that state with [tex]\left|\mathbf{r}\right\rangle[/tex], which is an eigenstate of the position operator with eigenvalue [tex]\mathbf{r}[/tex]. Thus I'm referring to the wavefunction in the position representation.
  6. May 12, 2008 #5
    Thanks, I haven't done much with Bra/ket notation!
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