| DATE: |
2007-02-28 16:00 - 17:00 |
| PLACE: |
Kenkyu Honkan 3F RM 321 |
| TITLE: |
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanic |
| CONTACT: |
tsuda |
| SPEAKER: |
Satoru Odake (Shinshu University) |
| LANGUAGE: |
Japanese |
| ABSTRACT: |
The annihilation-creation operators of the harmonic oscillator, the basic and most important tools in quantum physics, are generalized to most solvable quantum mechanical systems of single degree of freedom including the so-called `discrete' quantum mechanics. We present unified definition of the annihilation-creation operators (a^{(\pm)}) as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. These a^{(\pm)} are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. We also explain the shape invariant quantum mechanical systems.
Refs: S.Odake and R.Sasaki, Phys.Lett. B641(2006)112-117 (quant-ph/0605221); J.Math.Phys. 47(2006)102102(33pages) (quant-ph/0605215); Prog.Theor.Phys. 114(2005)1245-1260 (hep-th/0512155); J.Math.Phys. 46(2005)063513(10pages) (hep-th/0410109); J.Nonlinear Math.Phys. 12 Suppl.1(2005)507-521 (hep-th/0410102). |
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