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Classical limit of the path‐integral formulation of quantum mechanics in terms of the density matrix

 

作者: Pimon Ajanapon,  

 

期刊: American Journal of Physics  (AIP Available online 1987)
卷期: Volume 55, issue 2  

页码: 159-163

 

ISSN:0002-9505

 

年代: 1987

 

DOI:10.1119/1.15236

 

出版商: American Association of Physics Teachers

 

关键词: QUANTUM MECHANICS;FEYNMAN PATH INTEGRAL;DENSITY MATRIX;SCHROEDINGER PICTURE;BOUNDARY CONDITIONS

 

数据来源: AIP

 

摘要:

Instead of regarding the classical limit as the limit ℏ→0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. The derivation of the classical limit of quantum mechanics is carried out in two stages. First, the statistical classical limit is derived, and then, with an appropriate initial condition, the deterministic classical limit is obtained. The derivation hinges on the use of the Feynman path‐integral formulation of quantum mechanics in terms of the density matrix. It is shown that deterministic (Hamilton’s or Newton’s) classical mehanics is not the classical limit of Schrödinger’s wave mechanics. The classical limit of Schrödinger’s wave mechanics is only statistical and corresponds to the classical Liouville equation. In order to obtain the deterministic classical limit, it is necessary to start out initially with a quantum mechanical mixture.

 

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