An Analysis of the Quantum Liouville Equation

P. A. Markowich, Christian Ringhofer

Research output: Contribution to journalArticle

33 Citations (Scopus)

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

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Liouville equation
Liouville Equation
Semigroup Theory
Classical Limit
Existence and Uniqueness Results
Potential energy
Tend
Converge
Zero
Energy

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

Cite this

An Analysis of the Quantum Liouville Equation. / Markowich, P. A.; Ringhofer, Christian.

In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 69, No. 3, 1989, p. 121-127.

Research output: Contribution to journalArticle

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