# A Textbook on Modern Quantum Mechanics

- Available for pre-order. Item will ship after August 5, 2021

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## Book Description

New tools of presentation and mathematical treatment emerged and the subject matter of quantum mechanics has gone through significant changes, over the past decades. **A text book 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 and as solved examples. Fundamental discoveries that are the foundation of modern quantum mechanics, solution of Schrödinger’s wave equation for 1D problems and their importance, matrix and vector formulation of quantum mechanics, transformations, symmetries and conservation laws, angular and spin momenta, solution and application of Schrödinger equation to central potentials, time-independent perturbation theory, variational method, WKB approximation, quantum theory of scattering, many-particle systems and their quantum mechanical treatments, time-dependent perturbations and the interaction of fields with matter, relativistic quantum mechanics, quantization of fields and the second quantization are covered in the book. The contents of book are divided into 12 chapters. Some of the special features of book are:

- It provides everything a student needs to know for succeeding at all levels of the under graduation and graduation studies.
- It covers most of the topics that are taught udder (a) elementary, (b) intermediate , and (c) advance courses of quantum mechanics, across the various universities/colleges.
- It has detailed and elegant mathematical treatment with contemporary style of interpretation and presentation in simple English.
- Solved examples and unsolved exercises are made part of each chapter to consolidate the readers' understanding of fundamental concepts.
- The subject matter of the book is well tested on the students taught by the author over a period of 30 years.

It will serve as a valuable textbook to the students who enrol for Bachelor of Science , Master of Science, and Doctor of Philosophy (Ph.D.) degrees in the subjects of Physics, Chemistry and material science across the various Universities/Institutions in India, south Asian countries, USA and Europe.

## Table of Contents

Introduction to Quantum Mechanics. Black Body Radiations and Plank’s Hypothesis. Photoelectric effect. Bohr’s atomic model and Hydrogen atom. Compton scattering of photons. de Broglie hypothesis. Pauli Exclusion Principle. Schrödinger Wave Equation. Born interpretation of Wave Function. Heisenberg Uncertainty Principle. Davison and Germer Wave Properties of Electrons. Bohr-Sommerfeld Quantization Condition. Correspondance Principle. Heisenberg Quantum Mechanics. Dirac Theory of Quantum Mechanics. Important Quantum Mechanical Parameters in SI Units. Solved Examples. Exercises. **Wave Mechanics and its simple applications**. Schrödinger equation. Bound States and Scattering States. Probability density, probability current and Expectation Value. Simple applications of time independent Schrödinger equation. Periodic Solids and their Band Structures. Solved examples. Exercises. **Matrix Formulation of Quantum Mechanics**. Definitions and their basic Algebra. Bra and Ket notations. Vectors and Vector Space. Gram-Schmidt method for Orthogonalization of Vectors. Schwarz Inequality. Linear Transformation of a Vectors. Inverse matrix. Orthogonal matrix. Hermitian Matrix. Unitary Matrix. Diagonalization of a Matrix. Cayley-Hamilton theorem. Bilinear, Quadratic and Hermitian forms. Change of Basis in a Vector Space. Infinite-dimensional Space. Hilbert Space. Statement of Assumptions of Quantum Mechanics. General Uncertainty Principle. One Dimensional Harmonic Oscillator. Solved Examples. Exercises.** Transformations, Conservation Laws and Symmetries. **Translation in Space. Translation in Time. Rotation in Space. Quantum Generalization of the Rotation Operator. Invariance and Conservation Laws. Parity and Space Inversion. Time-Reversal Operator. Solved Examples. Exercises**. **Angular momentum**. **Orbital Angular Momentum**.** Eigenvalues of Angular Momentum**. **Eigenfunctions of Orbital Angular Momentum. General Angular Momentum. Spin Angular Momentum. Addition of Angular Momentum*. *Solved Examples. Exercises**. Schrödinger Equation for Central Potentials and 3D System**. Motion in a Central Field. Energy Eigenvalues of Hydrogen Atom. Wave functions of Hydrogen Atom. Radial Probability Density. Free Particle Motion. Spherically Symmetric Potential Well. Electron Confined to a 3D Box. Solved Examples. Exercises. **Approximation Methods. **Perturbation Theory. Variation Method.** **The W K B Approximation.** **Solved Examples. Exercises

**. Quantum Theory of Scattering**. Scattering Cross Section and Frame of Reference. Asymptotic Expansion and Scattering Amplitude. Partial Wave Analysis. Expression for Phase Shift. Integral Equation. Born Approximation. Transformation from Centre of Mass Coordinate system to Laboratory Coordinate System. Solve Examples. Exercises

**. Quantum Theory of Many Particle Systems**. System of Indistinguishable Particles. The Helium Atom. Systems of N-Electrons. Solved Examples. Exercises

**. Time dependent Perturbations and Semi-classical Treatment of Interaction of Field with Matter**. Time-dependent Potentials. Exactly Solvable Time-dependent Two-State Systems. Time-dependent Perturbation Theory. Harmonic Perturbation. Constant Perturbation. Semi-classical Treatment of Interaction of Field with Matter. Spontaneous Emission and Einstein Coefficients. Dipole Selection Rules. Solve Examples. Exercises.

**Relativistic Quantum Mechanics**. Klein-Gordon Equation. The Dirac Equation. Free Particle Solutions of Dirac Equation. Dirac Equation and the Constants of Motion. Spin Magnetic moment ( Dirac Electron in Electromagnetic Field). Spin-Orbit Interaction Energy. Solution of Dirac Equation for Central Potential . Solved Examples. Exercises

**. Quantization of Fields and Second Quantization.**Quantization of Electromagnetic Field. Second Quantization. System of Weakly Interacting Bosons. Free Electron system. Solved Example. Exercises.

## Author(s)

### Biography

Dr. A C Sharma is retired professor of Physics from the faculty of science, The Maharaja sayajirao University of Baroda, Vadodara ( Gujarat) India. He has been head of physics department , Dean of faculty of science for two terms, chairman of board of studies in Physics, chairman of faculty board for two terms, and the coordinator of DST-FIST & PURSE programmes and UGC DSA programme. He has distinguished educational records, obtained his Ph.D. from Roorkee University ( now IIT Roorkee) and did his post-doctoral work at Cavendish laboratory , University of Cambridge ( U K). Professor Sharma has served as scientists pool officer at IIT Delhi , lecturer at Jiwaji University Gwalior and then reader & Professor at Maharaja Sayajirao University of Baroda. He has also been a visiting scientists to Chalmers University of Technology, Sweden , Peking University, Beijing, China, and Indian Institute of Science, Bangalore. He has 33 years’ experience of teaching to undergraduate, post-graduate and graduate students and 40 years’ research experience in different areas of theoretical condensed matter physics. Semiconductors, surfaces and interfaces, superconductivity and nanostructures have been the areas of his research interests. Many-particle theory and numerical computations have been his expertized techniques to perform the research work. He has published 125 research papers. Some of his research papers are published in Journals like Physical review, Journal of condensed Matter Physics, Journal of Applied Physics and solid state communications. Professor Sharma has successfully completed 8** **major research projects, delivered 41 invited talks at national & international conferences, organised 6 conferences , and supervised 12 students for their Ph.D. degree. He has been awarded merit scholarship , University Bursary , College Gold Medal for undergraduate and post-graduate degrees, junior research fellowship , University of Cambridge’s Post-doctoral research assistantship , Madhya Pradesh Council of Science & Technology's Fellowship for in service Young Scientists , theoretical physics Seminar circuit speakership, and Indian National Science Academy visiting fellowship . Professor Sharma is member of Indian Physics Association, and a Fellow of Gujarat Science academy. He has worked as subject expert to evaluate the graduate thesis and research proposals for serval universities / institutions.