An Analysis of the Quantum Liouville Equation

Peter Markowich*, C. A. Ringhofer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


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 ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Issue number3
StatePublished - Jan 1 1989

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics


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