Quantum Hamilton-Jacobi Formalism

The Hamilton-Jacobi formalism of quantum mechanics is discussed in this book, which provides an approach to computing eigenvalues of quantum mechanical potential problems without solving for the wave function. It includes examples of exotic potentials and discusses complex zeros of the wave function, offering insights for advanced undergraduates and young researchers.

Format: Paperback / softback
Length: 112 pages
Publication date: 06 October 2022
Publisher: Springer International Publishing AG

This book delves into the intricate realm of quantum mechanics, unveiling the Hamilton-Jacobi formalism, a powerful tool for computing the eigenvalues of quantum mechanical potential problems. By bypassing the need to solve for the wave function, it enables the computation of these crucial values. The examples presented encompass a wide range of exotic potentials, including quasi-exactly solvable models and Lame potentials, each offering valuable insights into the nature of solutions. A meticulous application of boundary conditions unveils the underlying principles governing the behavior of these potential models. For advanced undergraduates with a solid grasp of complex variables and quantum mechanics, this book presents an intriguing approach to obtaining the eigenvalues and eigen-functions. Furthermore, the discussion on complex zeros of the wave function yields fascinating new results that hold relevance for advanced students and young researchers. Additionally, a few open problems in research are explored, presenting a formidable challenge to mathematically inclined readers. This comprehensive exploration of the Hamilton-Jacobi formalism and its applications in quantum mechanics provides a valuable resource for scholars and enthusiasts alike.

Weight: 209g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031106231
Edition number: 1st ed. 2022