An Essentially Singular Classical Limit

✍ Scribed by John Stalker

• Book ID: 102562525
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 85 KB
• Volume: 143
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1998.1799

✦ Synopsis

A simple variant of the problem of a particle in a box is shown to have an essential singularity in the classical limit h Ä 0.

1999 Academic Press

A particle in a box is in its ground state. The walls of the box are suddenly removed. After a time T has elapsed they are restored. What is the probability that the particle is again in the box and in its ground state? Classically, of course, the least energy state is one of rest and the probability is one. Quantum mechanically the probability should be rather less.

To specify the problem uniquely we specify that the box is one-dimensional and of length L, that the particle is of mass m and evolves according to the (non-relativistic) Schro dinger equation, and that the boundary conditions are the Neumann conditions. Dimensional analysis shows that the probability depends only on the dimensionless quantity