These videos show how raising and lowering operators are defined and used for the one-dimensional harmonic oscillator (1DHO). It uses the same notation as Griffiths, chapter 2.
The two key equations you need in order to use the operators are:
a−|n⟩=√n|n−1⟩,
a+|n⟩=√n+1|n+1⟩.
This is shown at about 24:25 of the third video (using a- a+). Everything before that is derivation.
Subscribe to:
Post Comments (Atom)
Midterm 2 solutions
Here are solutions to midterm 2. I see that I did not write it in the solutions, but it is helpful for sp2 type integrals to recall that \(\...
I think the residues are sqrt(n) for a- and sqrt(n+1) for a+. Easy thing to forget, I did the same thing on my first try.
ReplyDeleteAgree! Is there a specific mistake in a video on that?
DeleteI see what you mean now. In the last video there is a mistake.
DeleteHopefully everyone can find that. In the evaluation of the 2|2 term.
DeleteThe two key equations you need in order to use the operators are:
Deletea−|n⟩=√n|n−1⟩,
a+|n⟩=√n+1|n+1⟩.
This is shown at about 24:25 of the third video (using a- a+). Everything before that is derivation.
Hi Nick. I am not sure exactly where you mean in the third video. The part at 24:25 is correct and uses The two key equations you need in order to use the operators are:
Deletea−|n⟩=√n|n−1⟩,
a+|n⟩=√n+1|n+1⟩.
so, yes, you do want the square root.
DeleteThe two key equations you need in order to use the operators are:
ReplyDeletea−|n⟩=√n|n−1⟩,
a+|n⟩=√n+1|n+1⟩.
This is shown at about 24:25 of the third video (using a- a+). Everything before that is derivation.