Timeline for Characterizing the harmonic oscillator creation and annihilation operators in a rotationally invariant way
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2010 at 22:48 | answer | added | Zhang Jiang | timeline score: 1 | |
| Aug 12, 2010 at 14:20 | answer | added | David Bar Moshe | timeline score: 1 | |
| Aug 10, 2010 at 7:46 | vote | accept | Otis Chodosh | ||
| Aug 10, 2010 at 6:21 | history | edited | Charles Matthews | CC BY-SA 2.5 |
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| Aug 10, 2010 at 0:53 | answer | added | José Figueroa-O'Farrill | timeline score: 4 | |
| Aug 9, 2010 at 23:26 | comment | added | Victor Protsak | I'm not sure what kind of charact. is desired here. Creation and annih operators span a Heisenberg Lie algebra, which acts on $V=L^2(\mathbb{R}^2)$ (this is the inf version of the Stone-von Neumann rep of the Heisenberg group). Fixing the span $C$ of the annih operators is equivalent to fixing the 1-dim subspace spanned by the vacuum vector (their joint ker). Both $C$ and $C^+$ are $n$-dimensional subspaces of End $V$ stable under the conjugation action of $O(n),$ forming 2 copies of its vector representation. Howe-Tan's book approaches the subject from a representation-theoretic angle. | |
| Aug 9, 2010 at 22:28 | history | asked | Otis Chodosh | CC BY-SA 2.5 |