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.

scholarly journals Path Integrals, Spontaneous Localisation, and the Classical Limit

2020 ◽  
Vol 75 (2) ◽  
pp. 131-141 ◽  
Author(s):  
Bhavya Bhatt ◽  
Manish Ram Chander ◽  
Raj Patil ◽  
Ruchira Mishra ◽  
Shlok Nahar ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Path Integral ◽  
Classical Limit ◽  
Measurement Problem ◽  
Path Integrals ◽  
Path Integral Formulation ◽  
Von Neumann ◽  
Matrix Evolution ◽  
Grw Model

AbstractThe measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

scholarly journals A comparative review of four formulations of noncommutative quantum mechanics

2016 ◽  
Vol 31 (19) ◽  
pp. 1630025 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Path Integral ◽  
Heisenberg Algebra ◽  
Noncommutative Quantum Mechanics ◽  
Comparative Review ◽  
Noncommutative Quantum

Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl–Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.

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 Path Integral Quantization of Regular Lagrangian

2018 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Ola A. Jarabah
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Integral Method ◽  
Separation Of Variables ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Jacobi Function ◽  
Path Integral Quantization ◽  
Separation Of Variables Method ◽  
Path Integral Method

Path integral formulation based on the canonical method is discussed. The Hamilton Jacobi function for regular Lagrangian is obtained using separation of variables method. This function is used to quantize regular systems using path integral method. The path integral is obtained as integration over the canonical phase space coordinates. One illustrative example is considered to demonstrate the application of our formalism.

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