Parabolic Connection Formulae in Quantum Mechanics

✍ Scribed by L.V. Chebotarev

• Book ID: 102561608
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 441 KB
• Volume: 255
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1996.5663

✦ Synopsis

The mathematical structure of the tunnelling state of a quantum particle is established with respect to a large variety of smooth potential barriers, without any restriction upon the particle's coordinate or the barrier penetration integral (the latter is allowed to be arbitrarily small). Complete sufficient conditions for the semiclassical parabolic connection formulae are derived, both with respect to the particle's energy and relative to its coordinates. Explicit error bounds to these formulae are obtained. Extension to the overbarrier range is discussed.