Preface

The classical mechanics, so profound and successful in describing physical systems at macroscopic level, cannot do justice to describing systems at microscopic level. This is so because the experiments on microscopic particles put them under additional (and imprecisely known) forces of the probe used, which are really not included in the equation of motion of classical mechanics. And therefore the predictions of classical equation of motion do not tally with the experimental results on microscopic particles. This is not the only setback to a fresher. In addition to this, the experiments on microscopic particles (electrons, neutrons, protons, atoms etc.) reveal that these microscopic objects manifest themselves in (some) form of waves. With these two facts (which may not be unrelated), the emergence of an entirely new mechanics is imminent where both the above mentioned aspects that is, (i) the role of (additional) forces (during the process of measurement), and (ii) the wave nature of microscopic objects, are taken into account. The new mechanics emerges in the form of quantum mechanics.

Students even at (high) school level know that the physical world consists of microscopic objects like electrons, protons, neutrons, atoms, molecules etc. To understand behavior of physical system at macroscopic level, it is essential to understand behavior of the constituent microscopic particles. So a working knowledge of quantum mechanics (which is really the mechanics to study behavior of microscopic particles) is essential not only in the study of various branches of physical science (physics, chemistry, material science etc.) but also in the study of technology (solid state devices, quantum electronics, molecular devices etc.).

The objective of the present book is two-fold. Firstly, the beginner is exposed to the logical developments along with the experimental results on microscopic particles which lead to the operator mechanics or quantum mechanics in the form of Schrodinger equation. It is argued in details why operator mechanics is necessary to have a correspondence between theoretical results (of operator mechanics) and the experimental results on microscopic particles. We have discussed here the statistical/ensemble interpretation of the wave function ψ(r, t) as well as of expectation values of various operators. The rest of the book is devoted to the second objective: application of Schrodinger equation to various simple systems. For example, in a few chapters we have discussed one-particle systems where Schrodinger equation can be solved exactly. These include the cases of a particle in a potential box, potential well, harmonic potential etc. and the hydrogen atom problem. Then next few chapters are devoted to the cases where Schrodinger equation is not exactly solvable. Here, we discuss various approximate methods such as WKB method, time-independent and time-dependent perturbation method and the variational method. In the end we devote two chapters, to ‘Theory of Measurement in Quantum Mechanics’ and ‘Quantum Computing’. It may not be over emphasized that all undergraduate students are expected to become familiar with the principles of quantum mechanics, with approximation methods and also with the application of these methods to various phenomenon in atomic physics, nuclear physics, solid state physics and solid state devices etc. We have a large number of applications of quantum mechanics with examples from atomic physics, nuclear physics and solid state physics. In each chapter, we have added a number of problems along with solutions. The book is meant for both category of students, (i) for the beginners in quantum mechanics pursuing their B.Sc. (Pass, Honors)/B.Tech courses, and (ii) for students who use quantum mechanics to study systems like nuclei, atoms, molecules and solids in M.Sc. (Physics, Chemistry) courses.

Ever since I came across two excellent books (i) ‘Quantum Mechanics’ by D. Bohm and (ii) ‘Feynman Lectures on Physics Vol III’ in early seventies, I became more interested in Quantum Mechanics. I was lucky enough to get a chance to start my research work in the field of ‘strongly correlated electronic systems’, where quantum theory of many-particle systems is used throughout. I am indebted to my mentor and teacher Professor S.K. Joshi (Ex D.G., C.S.I.R., New Delhi) who initiated me to this research field, trained me in this field and has been a source of inspiration throughout my research and teaching career. I am thankful to my senior colleague and friend Professor Deepak Kumar (School of Physical Sciences, JNU, New Delhi) with whom I have always had fruitful and enjoyable discussions on quantum mechanics and condensed matter physics. Let me thank Professor M.A.B. Whitaker (Queen’s University, Belfast, N. Ireland) with whom I had fruitful discussions on quantum mechanics, specially during our collaborative work on ‘Measurement Process in Quantum Mechanics’, while I was on a post-doctoral assignment at New University of Ulster, N. Ireland in eighties. I have had numerous discussions with my old and new colleagues here in Physics Department on various aspects of quantum mechanics. I have benefitted with these discussions. Also I got full cooperation and support from all colleagues of the Department. I am really thankful to all of them.

I got interested in Physics, in the first place, due to my elder brother Shri. Shivraj Singh Tyagi, the first science graduate in my home town, who introduced me to the fascinating world of Science/Physics in my school days. I am really indebted to him. I thank my elder brother Shri. Satya Prakash Tyagi who taught me how to face realities of life. It has been more than three and a half decades now since I have been teaching courses like ‘Quantum Mechanics’, ‘Quantum Field Theory’, ‘Quantum Statistical Mechanics’ and ‘Quantum Theory of Solids’ to M.Sc. classes and ‘Quantum Physics’ to B.Tech classes at IIT Roorkee. I have learnt from the discussions on Quantum Mechanics with my students. Many a times their penetrating questions and sometimes even innocent questions made me to seek more simpler explanations of some quantum phenomenon. I was planning to write an introductory book on Quantum Mechanics since long. I had written a few chapters a decade back. It was only at the initiation of my wife Smt. Suman, that I could re-start writing work. Therefore the whole credit of this book is seeing the light of the day goes to her. Both my sons Professor Himanshu (IIT Ropar) and Priyank (TCS, Pune) helped me in many ways in this project and encouraged me to complete the work within the target time. I am really thankful to both.

I hope readers shall enjoy reading quantum mechanics from the book. I shall welcome any suggestions/comments from the readers. I shall also be grateful to the readers if typographical errors (which might have crept in even with our utmost care) are brought to my notice. The editorial and production teams of Pearson Education took special interest in this project and I am thankful to all members for their cooperation. Specially, I am thankful to Ravi Vishwakarma and Vipin Kumar for their sincere and dedicated efforts throughout the project.

I have dedicated this book to the memory of my mother, Smt. Jainandi Devi, who brought me up and shaped my life by playing the role of both mother and father, after the untimely death of my father (Shri. Chandra Bhan Tyagi) when I was three years old. Her qualities of exceptional courage and high values are still guiding me.

Ishwar Singh Tyagi