HOW TO SELF LEARN QUANTUM MECHANICS

  

    Quantum mechanics is the subject that revolutionized the way we look into nature. Most modern-day applications find their roots in quantum mechanics. Be it from semiconductors to lasers the theoretical foundation rests on the quantum formulation.  The crazy thing about QM is it was developed by a lot of approximations, counter-intuitive thoughts and hypotheses, and hardcore mathematics. But the experimental evidence miraculously confirmed the trueness of the theory. Some of the ideas and postulates seem completely unacceptable when analyzed under the lens of classical mechanics but who thought the subatomic world is so absurd and perhaps that’s why Feynman said that "Nature is Absurd" in one of his quotes. Most of us get fascinated by QM for one or the other reason. It may be because of your freshman physics course which had some introductory chapters related to it which were interesting, or you read some New York best seller book on this topic with buzzwords or may be because of some popular science videos where the narrator explained Schrodinger's cat. . But in reality, Schrodinger's cat is not cute as it looks. You need a lot of patience and hard work to tame this cat. So in this article, I will give a brief idea on how to self-study QM at an introductory to intermediate level.

Major Prerequisite:

    The major prerequisite for the subject is the stronghold in mathematics and some understanding of classical mechanics (particularly Hamiltonian formulation ). So let me list down the topics you should know in sequence according to topics: 

1.  1.Calculus: A stronghold on calculus at the undergraduate level is essential. You can refer to books like Calculus by James Stewart or Calculus by Thomas are really good books. They teach subjects at an application level.   

2. Vector Calculus: You should be familiar with vector differential and vector integration also you should be familiar with Curvilinear coordinates (at least in spherical and cylindrical symmetry).

        

 3. Linear Algebra: This is the heart of quantum mechanics particularly matrix mechanics. You should know linear algebra at an intermediate level. A thorough understanding of abstract mathematical concepts will help to understand the subject better. You can read topics in parallel, once you are done with essential topics. 

4. Special Polynomials: Mainly this includes Hermite polynomial, Legendre Polynomial, Spherical Harmonics, Laguerre Polynomial, Bessel functions, Neuman and Hankel functions.!! Scary right.. Don’t worry you need not know all these topics in-depth at beginners or intermediate level. You need to know some important subtopics like recursion relation, generating function, orthogonality concepts, and other essential topics required to understand the subject. This will also help in solving problems also. Most of the books on quantum mechanics(which I will be listing down) covers the topic up to the required level. But if you have an urge to know things in detail you can refer to any books on Mathematical physics like Arfken-Weber, Riley-Hobson, or even web notes with a  little google search.

5     5.Basic knowledge of Probability and Statistics: Again this is covered in most of the textbooks up to the required level. But I recommend a small digression will be very helpful to understand the subject in a better manner.  Topics like probability distribution, cumulants, mean-variance standard deviation, fundamental theorems of probability is the bare minimum. Don’t worry if you couldn’t do it. Once you start to learn QM, concepts of probability will be much better since you are applying probability for the first time in some real applications other than tossing coins and picking balls of various colors which you are hearing from high school maths.  

Now let us begin with course material and resources. I like to tell you that there isn’t a fixed set of books for the subjects and everyone’s approach is different. But let me classify books and video resources based on their content and complexity. I will try to give a brief highlight of the book.

1.Introduction to Quantum Mechanics by D.J Griffith: This is an absolute beginners book that is dedicated to Quantum mechanics (I didn’t consider Modern physics books like Beiser.) The mathematical complexity can be handle by any beginner with a little effort. The problems are really helpful to understand the subject  But I personally didn’t like how Griffith introduced the subject. There isn’t much historical introduction like what led to QM rather he starts directly with quantum mechanics. Also, the mathematical formulations are taught as required by the chapter which doesn't give an overall picture or overview of the topic. If you are a fan of Griffith’s Electrodynamics then I am sorry to say Prof.Griifth disappoints you here.

2. Quantum Mechanics Concept and Application by N.Zettili: This is another famous book in recent times since it was published just 10-15 years ago compared to other books. The book is a perfect fit for the intermediate level. It starts with a historical introduction to QM, later follows how quantum mechanics differ from classical mechanics. He introduces mathematical formulation in a detailed manner. He even dedicates two chapters to mathematical formulation. Later he moves onto 1-D problems and SHO; followed by moves onto Angular momentum algebra is followed by Hydrogen atom. This book has some good solved problems as well as exercises which are very helpful in understanding the subject. Also, it is quite helpful in the major physics entrance examination for masters and Ph.D. The major drawback I found was there isn’t much about the application of QM in other physical systems like you find in Shankar or Sakurai and the description of some topics is inadequate.  But as an entry-level book, this definitely finds a place in your study table.

3. Principles of Quantum Mehcnisi by R.Shankar: Prof Shankar famously known for his classes with wit and jokes teaches you the subject in the best possible way. I don’t recommend this for absolute beginners but still, you can manage with little effort. He starts with absolute basic slowly take into realms of QM, introducing to different applications on the way. Topics like path integral formulation, Qm of many particles are also covered in a good manner. The examples are very intuitive. The mathematical formulation given in the book is enough to understand the entire book. You will feel that Prof.Shankar is explaining things in presence sitting next to you. The main highlight of this book is it rigorously covers topics with adequate explanation and applications. You won't find any problems in this book compared to others but most of the problems are of quite a higher level which will make your concepts crystal clear. This book is strongly recommended to master QM.

4. Modern Quantum Mechanics by S.S Sakurai: This is another great book. The topics are organized unconventionally. He starts with direct concepts of spin to illustrate how QM systems differ from their classical counterpart. It is a small yet concise book. You will find path integral formulation, elementary concepts of group theory at a much earlier stage compared to other books. The approach of the book is quite different. There are some really good problems at the end of each and every chapter and some solved problems in between. The types of application you will find relay fascinates you and will understand how QM works in real physical systems. So I least recommend this book if you haven’t touched QM before. 

5. Quantum Mechanics by Cohen-Tannoudjji: This book by the Nobel laureate is a Magnum opus of QM. It is a complete Tour-de Quantum world. I am running out of metaphors to describe this book. It is a mammoth book comprising of two volumes(with each volume comprising 900 pages). Let me remind you it's not used as a textbook in general but as a reference book. The topics are well structured. First, he explains the essential theory and theoretical formulations related to the subject. At the end of each chapter, he covers the application of the same chapter as the appendix. You will find most of the applications which teaches you real-life physics. So I don’t think one can finish this book in a limited time, But definitely give it a try on relevant topics whenever you need.

Video Resources :

    There are more than 20 lecture series available for this subject from different universities across the internet. But I am only gonna consider the following resources which I found very helpful among many videos available. I have considered the lecture series which covers most of the topics at intermediate level. I like to know in the comment section if you find any video/lecture series helpful please mention it.  I like to add it here.

1. Lecture Series by Prof.Alan Adams: Prof. Alan Adam starts from absolute beginners level land I recommend this course for beginners. He makes the transition from classical to the quantum world in a smooth manner which is quite interesting. The good thing about the lecture is he also covers some of the application topics related to condensed matter theory and statistical mechanics. 

2. Lecture Series by Barton Zwiebach: This is another famous series by MIT professor which comprises of two-semester courses (the latter part of the second series covers some of the advanced topics ). I really liked the way he introduces you to the subject. He explains mathematical concepts in a real sense which helps to visualize quantum mechanics in a different manner which you don’t find generally in other lectures. The videos are short(compared to other lecture videos of 1hour) and consists of several parts. 

                    

3.Prof.V.Balakrishan: Who else can teach a subject with such a zeal other than Balki sir!! Though these are not intended for absolute beginners I recommend watching this after getting familiar with quantum mechanics. He gives a completely different perspective which elevates your thinking skills and approach to the subject. He also talks about the interlink between QM and other subjects. He covers the required mathematical parties

    So I recommend starting with Zettili and Shankar along with following any of the above-mentioned lecture videos. You can find the NPTEL series by Prof.Laxmi Bala, Prof. Ajoy Ghatak which are also equally good. But I found the above three quite better overall.

    Finally, I have some words of caution. At some stage, you may not find QM as juicy as expected the topics you see in pop-sci videos or the documentary feels rubbish once you really learn QM. At some times you might feel completely clueless about what you are learning, but hold on this was not only your problem. 

This is all about the introductory course on Quantum Mechanics. I will be posting a separate post on application-level topics like Perturbation Theory, Many Particles system, Quantum Scattering, and Relativistic Quantum mechanics. Please express your views and comments down. Thank You!! 

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