The propagator of the Calogero-Moser system in an external quadratic potential

✍ Scribed by M. Fleury

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 960 KB
• Volume: 28
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(98)00019-9

✦ Synopsis

We obtain the Hamilton operator of the Calogero-Moser quantum system in an external quadratic potential by conjugating the radial part for the action of SO(n) by conjugacy of the Hamilton operator of the quantum harmonic oscillator on the Euclidean vector space of real symmetric matrices. Then, with Mehler's formula, we derive the propagator of the problem. We also investigate some schemes to change the interaction constant. For two-particle systems, we obtain explicit formulae, whereas for many-particle systems, we reduce the computation of the propagator to finding a definite integral. We give also the short time approximation, the energy levels and the trace of the propagation operator.