Quantum Hamilton-Jacobi Formalism - A. K. Kapoor, Prasanta K. Panigrahi, S. Sree Ranjani

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Quantum Hamilton-Jacobi Formalism (eBook)

A. K. Kapoor, Prasanta K. Panigrahi, S. Sree Ranjani (Autoren)

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2022 | 1st ed. 2022
XV, 112 Seiten
Springer International Publishing (Verlag)
978-3-031-10624-8 (ISBN)

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This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allows

computation of eigenvalues of quantum mechanical potential problems without solving for the

wave function. The examples presented include exotic potentials such as quasi-exactly solvable

models and Lame an dassociated Lame potentials. A careful application of boundary conditions

offers an insight into the nature of solutions of several potential models. Advanced

undergraduates having knowledge of complex variables and quantum mechanics will find this

as an interesting method to obtain the eigenvalues and eigen-functions. The discussion on

complex zeros of the wave function gives intriguing new results which are relevant for

advanced students and young researchers. Moreover, a few open problems in research are

discussed as well, which pose a challenge to the mathematically oriented readers.

Ashok K. Kapoor served as a faculty member the School of Physics at the University of

Hyderabad from 1979 to 2012. In addition to the teaching and research, he served as the Head

of Special Centre of Integrated Studies, University of Hyderabad. He has taught undergraduate

and postgraduate courses in many other universities and excellent institutions. The institutions

where he served as a guest or a visiting faculty are the International Institute of Information

Technology (Hyderabad), the Shiv Nadar University, Noida, the Tata Institute of Fundamental

Research (Hyderabad Campus), the Birala Institute of Technology and Science (Hyderabad

Campus), the Indian Institute of Technology, Bhubaneswar and the Chennai Institute of

Mathematical Science. He obtained his Masters' degree in Physics from Allahabad University

and the Ph. D. from Indian Institute of Technology in Kanpur. His main research interests are

focused on quantum field theory, Hamilton-Jacobi formalism of quantum mechanics, and in

certain aspects of elementary particle physics phenomenology. He has written a textbook

on Complex Variables published by World Scientific and has collaborated in writing two

monographs on Stochastic Quantization.

Prasanta K. Panigrahi is a professor at the Indian Institute of Science Education and Research

Kolkata (IISER Kolkata), where he teaches and conducts research in theoretical physics in the

fields of Bose-Einstein condensate, quantum information and computing, quantum optics,

wavelet transform, and nonlinear dynamics. He obtained his Bachelor and Master of Science at

Ravenshaw College, Utkal University, Bhubaneswar, and Ph. D. at the University of Rochester,

New York, USA. He was a post-doctoral fellow at the University of Illinois at Chicago, USA, and

University of Montreal, Canada, and subsequently he joined the faculty at the University of

Hyderabad. He served as the Division Head of Quantum Information and Quantum Optics at

the Physical Research Laboratory, Ahmedabad, and as the Head of Department of Physical

Sciences, and Dean of Faculty Affairs at IISER Kolkata. He was also the officiating Director of the

Institute and Dean of International Relations and Outreach. He was ranked among the top ten

Indian Science Personalities in 2017, primarily for his work on the development of an artificial

intelligence-based algorithm which helps in diagnosing early-stage cervical cancer. He has

broad interests in different branches of science and enjoys collaborating with experimentalists.

S. Sree Ranjani is currently working as a content acquisition lead for the STM journals in the

Elsevier Publishing company. She has obtained her Ph. D. from the University of Hyderabad

(UOH) in 2005 in Physics. She has post-doctoral research experience from the Indian Institute of

Technology, Madras (IIT Madras). She was awarded a research associateship by the Council of

Scientific & Industrial Research (CSIR), India followed by a three-year research fellowship under

the Fast-track scheme for young scientists, by the Department of Science and Technology (DST),

Govt of India. Before switching to publishing, she taught physics to under-graduate,

engineering and science, students at ICFAI foundation for Higher Education, Hyderabad for

almost a decade. During this period, she obtained a three-year grant for her research project

from the Science and Research Board (SERB), Govt of India, under the extramural research

grant. In addition to teaching she handled administrative responsibilities, which included the

Head of the Department, Physical Sciences and Associate Dean, Research. Her areas of interest

include study of various potential models in quantum mechanics, supersymmetric quantum

mechanics, quantum optics, nonlinear dynamics and integrable models. She is interested in

science popularizing programs and conducts science workshops for middle and high school

students, when time permits.

Erscheint lt. Verlag	5.10.2022
Reihe/Serie	SpringerBriefs in Physics
Reihe/Serie	SpringerBriefs in Physics
Zusatzinfo	XV, 112 p. 13 illus., 3 illus. in color.
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	classification of exactly and quasi exactly solvable models • complex Scarf-II potential and optical systems • exact quantization condition • exceptional orthogonal polynomials • PT symmetry • Quantum Hamilton-Jacobi Formalism • rational extension of potential models
ISBN-10	3-031-10624-5 / 3031106245
ISBN-13	978-3-031-10624-8 / 9783031106248

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