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An Analysis of the Quantum Liouville Equation
Author(s) -
Markowich P. A.,
Ringhofer C. A.
Publication year - 1989
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19890690303
Subject(s) - uniqueness , bounded function , semigroup , planck constant , constant (computer programming) , limit (mathematics) , mathematics , liouville equation , quantum , mathematical physics , liouville field theory , zero (linguistics) , fokker–planck equation , physics , mathematical analysis , quantum mechanics , differential equation , quantum gravity , linguistics , philosophy , computer science , relationship between string theory and quantum field theory , programming language
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.