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Il Nuovo Cimento B (1971-1996)

, Volume 79, Issue 2, pp 271–283 | Cite as

Hamiltonian vector fields in quantum mechanics

  • R. Cirelli
  • P. Lanzavecchia
Article

Summary

The set of pure states of an ordinary quantum-mechanical system has the structure of a Kähler manifold. As in classical mechanics, a vector field, called Hamiltonian, on this manifold is associated to the system. The equations induced by quantum-mechanical Hamiltonian vector fields are Schrödinger equations. A complete characterization of these vector fields is given and a quantum Liouville theorem is obtained.

PACS

02.40 Geometry differential geometry and topology 

Гамильтоновы векторные поля в квантовой механике

Резюме

Система чистых состояний для обычной квантовомеханической системы имеет структуру множества Кэлера. Как в классической механике, векторное поле, называемое гамильтоновым, на этом множетсве связано с рассматриваемой системой. Уравнения, индуцированные квантовомеханическими гамильтоновыми векторными полями, являются уравнениями Шредингера. Приводится полная характеристика этих векторных полей и получается квантовая теорема Лиувилля.

Riassunto

L’insieme degli stati puri di un sistema quantistico ordinario ha la struttura di varietà khäleriana. Un campo vettoriale su questa varietà, chiamato hamiltoniano, è associato, come nella meccanica classica, al sistema. Le equazioni indotte da campi vettoriali hamiltoniani quantistici sono equazioni di Schrödinger. Si dà una caratterizzazione completa di questi campi vettoriali e si ottiene un teorema di Liouville quantistico.

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Copyright information

© Società Italiana di Fisica 1984

Authors and Affiliations

  • R. Cirelli
    • 1
  • P. Lanzavecchia
    • 1
    • 2
  1. 1.Dipartimento di Fisica dell’UniversitàMilanoItalia
  2. 2.Istituto Nazionale di Fisica NucleareSezione di MilanoItalia

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