Digitale Medien
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
11 (1989), S. 459-469
ISSN:
0170-4214
Schlagwort(e):
Mathematics and Statistics
;
Applied Mathematics
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
Notizen:
We present a semigroup analysis of the quantum Liouville equation, which models the temporal evolution of the (quasi) distribution of an electron ensemble under the action of a scalar potential. By employing the density matrix formulation of quantum physics we prove that the quantum Liouville operator generates a unitary group on L2 if the corresponding Hamiltonian is essentially self-adjoint.Also, we analyse the existence and non-negativity of the particale density and prove that the solutions of the quantum Liouville equation converge to weak solutions of the classical Liouville equation as the Planck constant tends to zero (assuming that the potential is sufficiently smooth).
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1002/mma.1670110404
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