An Analysis of the Quantum Liouville Equation

P. A. Markowich; C. A. Ringhofer

doi:10.1002/zamm.19890690303

An Analysis of the Quantum Liouville Equation

P. A. Markowich^*, C. A. Ringhofer

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

41 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 language	English (US)
Pages (from-to)	121-127
Number of pages	7
Journal	ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Volume	69
Issue number	3
DOIs	https://doi.org/10.1002/zamm.19890690303
State	Published - 1989
Externally published	Yes

ASJC Scopus subject areas

Computational Mechanics
Applied Mathematics

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10.1002/zamm.19890690303

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title = "An Analysis of the Quantum Liouville Equation",

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.",

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doi = "10.1002/zamm.19890690303",

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AB - 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.

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DO - 10.1002/zamm.19890690303

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JO - ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

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ER -

An Analysis of the Quantum Liouville Equation

Abstract

ASJC Scopus subject areas

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