 One of the most important fields of study to ever exist is physics, because physics is the study of the entire universe, starting from the subatomic to the intergalactic. But within physics, if I say what is the most interesting, most fascinating subject for the branch of physics to study, it would definitely be quantum mechanics. Everything that you see around you, all the physical phenomena that you see in the classical macroscopic world, are but a subset, a special case of a more general quantum mechanical theory according to whose principles the universe works. So to know quantum mechanics is in a sense to know how the universe functions at a fundamental level. Therefore, I'm starting with a certain sense of responsibility and honor and due to the many requests that I've received from you guys over the period of months and years, finally a lecture series on quantum mechanics. Most of you are already familiar with me. I am Divya Jyotidas. I did my masters in physics from IIT Kanpur and then I taught for 10 years at University of Delhi. So the lecture series that I'm going to start is going to be based on the syllabi or the curriculum that most college and postgraduate students face in their university classes. In this video, because this is the introduction to this lecture series, I'm going to talk about first the syllabi of quantum mechanics, the approach that I'm going to follow, the sequence of topics, some of the difficulties that student face when studying this kind of a subject and what you can expect from this particular subject and this lecture series. First of all, what is quantum mechanics? You see quantum mechanics is a branch of physics that deals with a behavior of matter and energy at the most smallest of scales, at the scales of atoms and subatomic particles. And because of this reason, the principles of quantum mechanics lays the foundation of many branches of modern physics like solid state physics, atomic and molecular physics, particle physics, optics, thermodynamics, statistical physics, etc. In fact, even beyond the traditional definition of physics subjects, it lays the foundations for chemistry and biology. So you see how important this paper is. It has uses in many different kinds of technological advancements that is required for human civilization. For example, electronics, computers, communication and understanding of solid materials, which is required in all of these technological advancements and understanding of semiconductors, superconductors, lasers, applications in medical imaging. All of these different advancements requires on some level applications of the principles of quantum mechanics. So let me now give you a brief idea about the teaching methodology that I'm going to follow, the syllabus that I'm going to cover and the sequence of topics that I'm going to cover in the coming weeks and months. Now, usually there are two kinds of approaches that mint teachers follow when they teach this subject of quantum mechanics in a classroom. The first approach is to just go straight into the principles of quantum mechanics and start applying those principles in various systems. Now, this approach is quite common and perfectly valid because the principles of quantum mechanics represent an abrupt change from most classical systems. Therefore, just by introducing these ideas and going into applications is also a good way of learning the subject. I, on the other hand, like to follow a different approach. I usually like to follow the approach of what is called the historical development of these ideas. I like to break down the subject of quantum mechanics in a manner in which these historical ideas came into being. You see, quantum mechanics is one of those subjects that was not put forth by any one person. Like, for example, Isaac Newton gave us the laws of mechanics. Albert Einstein gave us the theory of relativity. Maxwell combined the equations of electrodynamics. Quantum mechanics, on the other hand, has come into reality because of the contributions of many different scientists over a period of decades. So, I love the sequence of studying the various topics in a manner that the historical progress has been made. So, for example, what were the assumptions at the end of the classical era in physics? What are the experiments that reveal to us how classical physics failed in explaining certain phenomena? What are the new ideas that came into picture to explain these kind of different experiments where classical physics failed? How the ideas of quantum mechanics came into picture? How they were combined together to create a theory? That is a sequence of topics that I usually like to follow. And in that sequence, I have divided the entire syllabi that I am going to cover into three different sections. You see, in college and university, when you study this particular paper, it is not a one semester paper. By the way, it spans over two or three semesters. Usually, in most colleges, you study initially a paper called Elements of Modern Physics, where you study the origins of quantum mechanics. And then maybe in your later years, you study a paper called Introduction to Quantum Mechanics, which gives you essentially the quantum mechanical principles. And if you go to university, like for a postgraduate program, you study advanced quantum mechanics. So, in that sense, I have divided the entire syllabus into three different sections. First is for beginner students, students who are right out of high school or going to college. For them, the first section is called the basics of quantum mechanics. So, in this section, I will basically focus on the various experiments where the classical explanations failed and quantum mechanical ideas arose to explain those kinds of experiments. For example, we will spend a lot of time discussing wave particle duality. And within that context, I will talk a lot about various experiments like blackbody radiation, photoelectric effect, competence scattering, pair production, de Broglie hypothesis, Davidson-Jermer experiment, two slit electron interference experiment, etc. Then we're going to talk about wave packets, group phase velocities, uncertainty relations, atomic structure, spectroscopy and lasers. This will give us a brief overview of the origins of quantum mechanics. Now, this is just a very concise collection of the topics. As I'm making these lecture videos, I will go quite in detail in each of these individual topics. So, every single topic might have more than one lectures required to explain them properly. Once the first origins of quantum mechanics is done, then I'll go ahead to the next section, which is introduction to quantum mechanics, which is suited for intermediate students, students who are in their undergrad. And here I will go straight into the subject of quantum mechanics. But I will make a clear distinction between two different approaches. You see, there are two different formalisms of studying quantum mechanics. One is the wave mechanical formulation given by Schrodinger. And the other is the matrix formulation of Heisenberg to study quantum mechanics. So, first, we will focus on the wave mechanical formulation of quantum mechanics. So, there we will study about the Schrodinger's equation, the probabilistic interpretation, normalization, expectation values, operators, etc. We will use the Schrodinger's equation to solve various kinds of potential problems like free particle in finite square well potential delta function potential, finite square well potential step potential quantum tunneling, etc. Once this is done, then I will introduce to you the matrix formulation of quantum mechanics. So, for that, we will require a couple of lectures on linear vector spaces, Hilbert space, Dirac notation, operators. And we will use this matrix formalism to solve problems of harmonic oscillator, angular momentum, etc. And once this section is done, then we will go ahead to the advanced quantum mechanics topics, which is, of course, for advanced students, mostly for students who are either at the later years of their undergrad program, or in a postgraduate course. So, we will talk about spin, stern, Gerlach experiment, identical particles, exclusion principle, perturbation theory, variational principle, WK approximation, Z-man effects, spin-operate interaction, addition of angular momentum. And if we have time and if you are interested, maybe some lectures on scattering and relativistic quantum mechanics. Once the entire syllabus of quantum mechanics is over, then we can spend some time if you are interested in on some additional topics, mostly philosophy of quantum mechanics, the measurement problem, EPR paradox, Bell's theorem, Schrodinger's cad, etc. So this is more or less a concise collection of all the topics that I'm planning to cover in this particular lecture series in the coming months. This is based on the pattern of the university curriculum that most universities across the world follow. And my focus on the subject is going to be very much conceptual and theoretical based as you would in a university program. Now, if you are studying this paper for the first time, then quantum mechanics is, to say the least, not an easy subject. It has its own difficulties. I have myself taught this paper for many years. And there are a number of difficulties that you as a student are going to face. So let's talk about those difficulties and see how we can overcome them. And can we even overcome them as we follow this sequence of topics in this particular lecture series? The first difficulty that students face is that of mathematical complexity. You see quantum mechanics is a very mathematical and abstract subject. Many times we have to rely on certain mathematical equations and procedures to come up with the answer. Therefore, if you want to understand this subject properly, you have to be good at certain concepts of mathematics. For example, calculus, differential equations, complex numbers, basics of probability theory, linear vector spaces, etc. The second difficulty, and I think by far the highest kind of difficulty that majority of the students face is that of conceptual understanding of the subjects or a visual understanding of the subject. You see, whenever we study something, we like to visualize that thing in our mind. But quantum mechanics in that sense is very difficult to visualize. Because quantum mechanical ideas represent abrupt and revolutionary departure from most classical phenomena, the kinds of concepts that we are going to study are very different and sometimes very confusing and frustrating to say the least. And you are going to face that if you're studying this paper. For example, if we talk about a topic like wave particle duality, you have light, which behaves like waves in certain experiments and particles in other experiments. You have traditional particles like electrons that behave like particles in some experiments and waves like other experiments. How do you reconcile that concept in your mind? So if we are talking about conceptual difficulty, because this is what you're going to face. Mostly one of that is wave particle duality. We will talk about it further. But there are many other such conceptual difficulties that you're going to face. For example, if we talk about quantum tunneling, that is something that you don't really see in the classical world. So your mind is not attuned to understanding topics like that. Even more quantum entanglement, uncertainty relations, the probabilistic interpretation of this particular subject. You see, when you study classical physics, we are very used to the idea of a particle tracing out a tragic tree through space. But quantum mechanics, we don't really talk about tragic trees. We don't talk about a particle being at a particular location, but we talk about probabilities associated with finding the particle if we make a measurement, which brings me to the measurement, the interpretation of what measurement means. Many of these topics are extremely revolutionary in the sense that you don't really get to see these concepts outside of quantum mechanics. And you will probably study them for the first time if you're studying this paper for the first time. And they are quite difficult to grasp and visualize, which will represent one of the major difficulties that you will face. But the question is, why is it so difficult to understand? You see, our brains have developed in the macroscopic classical world through evolution over millions of years. And because of that, our brains are used to looking at physical phenomena in a very classical sense. So for example, if I throw a ball in the air, just by looking at that ball for a couple of seconds, you will have an intuitive idea of how long it is going to take for the ball to reach the ground, how far it is going to fall, what velocity is going to fall. You don't need to sit there and do these calculations with some mathematical expression using a pen and paper, but you will have some intuitive understanding of it. This is why we have sports where people play cricket or people play football and they have an idea that where the ball is going, where to run this and that. Our brains are very used to these physical phenomena. If there is a car coming from this side, another car coming from this side, even seconds before the crash happens, we have an idea that, okay, if they're going at this angle at that speed, it's going to crash in sometime. So our brains are very much used to the classical world. But the quantum world, the microscopic world, is a very different world. Particles do not go around in tragic trees. In fact, particles are not really particles in the sense that we understand them in a classical world. It's a very murky, a very different kind of world and our brains have not evolved to understand those physical phenomena. Therefore, it is necessary to create a shift in our perspective of how we look at the physical phenomena because the microscopic behavior is vastly different from the classical behavior that we are used to. But don't worry, you are not the first, neither you are going to be the last student to face these kind of conceptual difficulties. Greater minds who have come before us faced these challenges. You know, Niels Bohr once said, if you're not confused by quantum mechanics, then you haven't really understood it. Richard Feynman famously said, I can safely say that nobody understands quantum mechanics. So some of the greatest minds who have come before us has faced these challenges. So you're not the first person to face these challenges. But keep in mind that these are the challenges that you will face and you will have to overcome. The next difficulty that you're going to face is kind of similar to the point number two, which is there's a lack of concrete examples that you're going to see when you study this particular subject. So most of our understanding of classical systems, behaviors of classical systems cannot be borrowed into the quantum mechanical world. Even though we try to do that sometimes, we can't really do that. And there's a lack of a concrete physical behavior or visualization that we have, which needs to be filled by mathematical complexities and principles. There you will face the same kind of a challenge. The last difficulty that many students will face, especially if you are in your postgraduate course and you want to do a dissertation in some quantum mechanical problem or you want to go into research, is that you will have to develop new skills because many of these problems are difficult to solve by hand. You will have to learn some kind of a software or computer programming or some kind of a numerical techniques to be able to solve various kinds of problems if you want to do research in the future, in this particular field. I will try to address all these problems as we go ahead. I'll try to publish around two or three lectures every week in the evening time, around 6 or 7 p.m. Indian Standard Time. And I will try to go in depth in all these topics that I just now mentioned in detail as much as I can. I will of course also require some feedback or suggestions from you. You can write in the in the comment section anything that I can help you with, any kind of a topic you want to add to the syllabus, any kind of an approach that you would like me to follow, any kind of a suggestion that you have, you can definitely give me in the comment section and I'll take that into account as we go ahead in this particular lecture series. You see quantum mechanics is one of the fascinating subjects as I said. I would in fact go so far as to say that if you don't know some degree of quantum mechanics your life is incomplete because quantum mechanics is on the edge of human knowledge. You know it is an understanding of how the universe works at its most smallest scales. Even if it is very confusing, even if it is difficult, even if it is sometimes frustrating we need to know that at the end of the day it is true. It is a theory that has proven itself to be successful over and over again in the last hundred years since its inception. As of today this is one of the successful theories in physics and remains a bedrock of modern physics. So in this lecture series my objective as a teacher is to not only communicate with you the knowledge and the information of this particular subject in a manner that you understand this subject but if possible also to communicate with you the beauty this subject has and the excitement that I feel for this subject if I can convey that to you even 10 percent then I would feel that I have done my job. So this is going to be quite a long journey I am really looking forward to it and good books are very important if you're studying a new subject and I'm going to recommend some good books in the upcoming video so stay tuned this is going to be an exciting series of lectures. I'm Divya Jyotidas I'll see you in the next video. Bye