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Il Nuovo Cimento A (1965-1970)

, Volume 62, Issue 2, pp 561–580 | Cite as

Accidental degeneracies and tridimensional potentials

  • M. Enriotti
  • M. L. Faccini
Article

Summary

The problem of the search for three-dimensional potentials possessing higher (accidental) symmetries is examined in the framework of a classical Hamiltonian theory. Under suitable restrictions a class of potentials leading to strictly periodical motions has been found for each of the eleven Eisenhart co-ordinate systems. Further, the separated Schrödinger equations, written for the above classical potentials, have been classified.

Keywords

Riemann Surface Closed Orbit Classical Potential SchrSdinger Equation Degenerate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Случайные вырождения и трехмерные потенциалы

Резюме

В рамках классической теории с гамильтонианом исследуется проблема отыскания трехмерных потенциалов, обладающих более высокими (случайными) симметриями. При соответствующих ограничениях был найден класс потенциалов, приводящих к точно периодическим движениям для каждой из одиннадцати систем координат Эйзенхарта. Затем была проведена классификация отдельных уравнений Шредингера, записанных для вышеуказанных классических потенциалов.

Riassunto

Si esamina il problema della determinazione di potenziali tridimensionali che posseggono simmetrie accidentali nell'ambito di una teoria hamiltoniana classica. Con opportune restrizioni, si costruisce una classe di potenziali che conducono a moti strettamente periodici per ciascuno degli undici sistemi di coordinate di Eisenhart. Inoltre si dà una classificazione delle equazioni di Schrödinger separate, scritte per ciascuno dei potenziali classici trovati.

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Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • M. Enriotti
    • 1
  • M. L. Faccini
    • 2
    • 3
  1. 1.Istituto di Fisica Teorica dell'UniversitàParma
  2. 2.Istituto di Scienze Fisiche dell'UniversitàMilano
  3. 3.Scuola di Perfezionamento in FisicaMilano

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