A Textbook on Modern Quantum Mechanics

A C Sharma

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367723446
• eBook ISBN: 9781000421378
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Quantum Theory

Over the course of the past two to three decades, new tools of presentation and mathematical treatment have emerged and the subject matter of quantum mechanics has gone through significant changes. A Textbook on Modern Quantum Mechanics presents the selected elementary, intermediate, and advance topics with rejuvenated approach to the subject matter. Newly merged topics from contemporary physics and chemistry are included in the text as well as solved examples. The book covers: (i) fundamental discoveries that are the foundation of modern quantum mechanics; (ii) solution of Schrödinger's wave equation for 1D problems and their importance; (iii) matrix and vector formulation of quantum mechanics; (iv) transformations, symmetries, and conservation laws; (v) angular and spin momenta; (vi) solution of Schrödinger equation for central potentials; (vii) time-independent perturbation theory, variational method and WKB approximation; (viii) quantum theory of scattering; (xi) many-particle systems and their quantum mechanical treatments; (x) time-dependent perturbations and the interaction of fields with matter; (xi) relativistic quantum mechanics; and (xii) quantization of fields and the second quantization.

Key Features:

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• It provides everything a student needs to know for succeeding at all levels of the undergraduate and graduate studies.

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• It covers most of the topics that are taught under (a) elementary, (b) intermediate, and (c) advance courses of quantum mechanics at universities and colleges.

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• It has detailed and elegant mathematical treatment with contemporary style of interpretation and presentation in simple English.

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• Solved examples and unsolved exercises that are part of each chapter to consolidate the readers' understanding of fundamental concepts.

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• The subject matter of the book is well tested on the students taught by the author over a period of 30 years.

This is a valuable textbook for students pursuing Bachelor of Science, Master of Science, and Doctor of Philosophy (PhD) degrees in the subjects of Physics, Chemistry, and materials science in India, South Asian countries, the United States, and Europe.

1

Introduction to Quantum Mechanics

During the late 1800s and early 1900s, it became clear that physics was due for major revision. Existing laws of physics at that time failed to explain adequately or even approximately a large number of phenomena and observations. The explanation of phenomena involving small systems like electrons and atoms and their interaction with electromagnetic fields faced serious problems when attempted with classical physics. The following clearly demonstrated the necessity for a departure from classical mechanics:

1. Classical physics laws suggest that an electron moving in an orbit of an atom must lose energy by emission of synchrotron radiation, and it must spiral gradually towards the nucleus of an atom, which was not observed experimentally.
2. The experiments that were performed for observing the interference of light, the photoelectric effect, and diffraction of electrons clearly demonstrated that under certain situations waves act like streams of particles, and streams of particles were found to act as if they were waves. The laws of classical physics were completely unable to explain this.
3. The laws of classical physics suggest that the energy density of an electromagnetic field in vacuum cannot be finite because of the divergence of energy carried by short wavelength modes, which was not observed in experiments, and the total energy density was found to be finite.

Quantum mechanics, which was developed between 1900 and 1930 along with the general and special theory of relativity, completely revolutionized the field of physics, and it is now one of the pillars of modern sciences. The new concepts such as the wave properties of a particle and particle properties of radiation, quantized energy and momentum, and the idea that the position of a particle like an electron cannot be known exactly at any one instant of time had been found necessary to explain all the new experimental evidence that was available at that time. Classical mechanics and electromagnetism were replaced by quantum mechanics when a system was of a size comparable with that of an atom. Today, it is well understood that quantum mechanics is not only needed to des...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• About the Author
• 1. Introduction to Quantum Mechanics
• 2. Wave Mechanics and Its Simple Applications
• 3. Matrix Formulation of Quantum Mechanics
• 4. Transformations, Conservation Laws, and Symmetries
• 5. Angular Momentum
• 6. Schrödinger Equation for Central Potentials and 3D System
• 7. Approximation Methods
• 8. Quantum Theory of Scattering
• 9. Quantum Theory of Many Particle Systems
• 10. Time-dependent Perturbations and Semi-classical Treatment of Interaction of Field with Matter
• 11. Relativistic Quantum Mechanics
• 12. Quantization of Fields and Second Quantization
• Annexure A: Useful Formulae
• Annexure B: Dirac Delta Function
• Answers to Exercises
• Bibliography
• Index