Question about Dirac form

  • #1

Main Question or Discussion Point

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!

Thanks
 

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Answers and Replies

  • #2
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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.
 
  • #3
I am not familiar with that form... is that just Psi(r)? and what quantum numbers are the 0 and 1?
Thanks again!
 
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  • #4
410
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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.
 
  • #5
Thanks, I haven't done much with Bra/ket notation!
 

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