This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allowscomputation of eigenvalues of quantum mechanical potential problems without solving for thewave function. The examples presented include exotic potentials such as quasi-exactly solvablemodels and Lame an dassociated Lame potentials. A careful application of boundary conditionsoffers an insight into the nature of solutions of several potential models. Advancedundergraduates having knowledge of complex variables and quantum mechanics will find thisas an interesting method to obtain the eigenvalues and eigen-functions. The discussion oncomplex zeros of the wave function gives intriguing new results which are relevant foradvanced students and young researchers. Moreover, a few open problems in research arediscussed as well, which pose a challenge to the mathematically oriented readers.

Autorentext

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 quantummechanics, 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 atthe 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.