arXiv physics/01050742001-05-22physics.chem-phphysics.gen-ph

玻尔兹曼第三维里的超球绝热形式

Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial

Sigurd Yves Larsen

备注：: 7 pages, published in the Proceedings of the Bogolyubov Conference on Problems of Theoretical and Mathematical Physics (Moscow-Dubna-Kiev, September 27 - October 6, 1999)

摘要：

首先，我们证明，如果没有束缚态，我们可以表示的q.m.第三个集群-涉及3和更少的粒子在统计力学-作为一个公式，涉及绝热本征相移。这是玻尔兹曼统计。从这个Q. M。公式，在纯粹的排斥力的情况下，我们恢复，随着h趋于0，集群的经典表达式。然后，我们讨论的困难，出现在2体束缚态的存在下，并提出了一个试探性的公式，涉及本征相移和2和3体束缚态能量。我们强调，重要的困难尚未解决。

英文摘要：

First, we show that, if there are no bound states, we can express the q.m. third cluster - involving 3 and fewer particles in Statistical Mechanics - as a formula involving adiabatic eigenphase shifts. This is for Boltzmann statistics. From this q.m. formulation, in the case of purely repulsive forces, we recover, as h goes to 0, the classical expressions for the cluster. We then discuss difficulties which arise in the presence of 2-body bound states and present a tentative formula involving eigenphase shifts and the 2 and 3 body bound state energies. We emphasize that important difficulties have not been resolved.

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