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Paper   IPM / Physic / 6513
School of Physics
  Title:   A General Formulation of Discrete-Time Quantum Machanics: Restrictions on the Action and the Relation of Unitarity to the Existence Theorem for Initial-Value Problems
  Author(s):  M. Khorrami
  Status:   Published
  Journal: Ann. Phys.
  No.:  2
  Vol.:  244
  Year:  1995
  Pages:   101-111
  Supported by:  IPM
A general formulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the operators), are no longer present here. Then the criteria for the unitarity of the evolution operator are examined. It is shown that the unitarity of the evolution operator puts restrictions on the form of the action, and also implies the existence of a solution for the classical initial-value problem.

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