Quantization problem and variational principle in the phase‐space formulation of quantum mechanics

1976 ◽  
Vol 17 (10) ◽  
pp. 1863-1866 ◽  
Author(s):  
Leon Cohen
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Variational Principle ◽  
Space Formulation ◽  
Quantization Problem

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

scholarly journals The Phase Space Formulation of Time-Symmetric Quantum Mechanics

Quanta ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 27 ◽  
Author(s):  
Charlyne De Gosson ◽  
Maurice A. De Gosson
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Symmetric Quantum ◽  
Space Formulation ◽  
Time Symmetric Quantum Mechanics

Advanced Topics in Quantum Mechanics

2021 ◽  
Author(s):  
Marcos Mariño
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Path Integral ◽  
Worked Examples ◽  
Wkb Method ◽  
Path Integral Formulation ◽  
Graduate Courses ◽  
Advanced Students ◽  
Key Concepts ◽  
Space Formulation

Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.

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