An Analysis of the Quantum Liouville Equation

P. A. Markowich, Christian Ringhofer

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

We present an analysis of the quantum Liouville equation under the assumption of a globally bounded potential energy. By using methods of semigroup theory we prove existence and uniqueness results. We also show the existence of the particle density. The last section is concerned with the classical limit. We show that the solutions of the quantum Liouville equation converge to the solution of the classical Liouville equation as the Planck constant h tends to zero.

Original languageEnglish (US)
Pages (from-to)121-127
Number of pages7
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume69
Issue number3
DOIs
StatePublished - 1989

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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