The Schrödinger equation as a moving curve

✍ Scribed by Radha Balakrishnan; Rossen Dandoloff

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 82 KB
• Volume: 260
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00492-2

✦ Synopsis

We identify two types of local geometric phases associated with a moving space curve of arc length s, viz, the 'Fermi-Walker' and 'incompatibility' phases, and derive a relationship between them. The time-dependent Schrodinger Ž . equation for a particle in a potential V s,u , u denoting time, can then be interpreted geometrically as a moving curve whose Ž . Fermi-Walker phase density is given by y E VrE s . Examples of curve evolution corresponding to wave-packet solutions for a free particle and a harmonic oscillator are presented.