TY - JOUR
T1 - An Analysis of the Quantum Liouville Equation
AU - Markowich, P. A.
AU - Ringhofer, Christian
PY - 1989
Y1 - 1989
N2 - 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.
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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U2 - 10.1002/zamm.19890690303
DO - 10.1002/zamm.19890690303
M3 - Article
AN - SCOPUS:84984038326
SN - 0044-2267
VL - 69
SP - 121
EP - 127
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
IS - 3
ER -