MSc JNU Delhi Specialized Topics: Classical Mechanics, Quantum Mechanics , Nuclear Physics and Atomic Physics.

I am a founder and faculty in the Pravegaa Institute in Delhi.

I like to teach classical mechanics and Quantum Mechanics at the Graduate and Post Graduate level.

My approach towards Teaching

**Classical Mechanics:**

Classical mechanics is a fundamental topic and an indispensable part of Physics. Itโs been a great honor to learn and teach the beautiful subject for the last 15 years. As a modest learner of the subject, as well as a teacher of a young mind, I feel it is my responsibility to educate students about classical mechanics through:

1) Qualitative analysis of physical systems across the concept of phase space and nonlinear dynamics.

2) Prepare them to understand different types of symmetry via Hamilton formulation, canonical, and Poisson bracket.

3) Formulate background of quantum mechanics and statistical mechanics through Hamiltonian formulation Poisson bracket and concept of action-angle.

I try to connect the basic concept of the classical state of the system to the Lagrangian formulation through the principle of least action. It is inspiring to share the importance of Hamiltonian formulation and then connect it to the mathematical formulation of Poisson bracket and canonical transformation.

Once I complete the formulation part, I try to use these concepts on small oscillation, Central force problem, and rigid body dynamics.

Special Theory of Relativity is one of the fundamental topics. I try to discuss four-dimension space-time coordinates through Lorentz transformation. Itโs challenging to discuss the measure of the physical quantity of the same event from two different inertial frames. The discussion of mass-energy equivalence is another jewel of the crown.

The discussion of four vectors, Minkowski space and invariant laws under Lorentz transformation, is an ecstatic part of my teaching and learning about the subject. Finally, I conclude my topic with the fundamentals of relativistic electrodynamics and relativistic quantum mechanics.

Two-way communication, understanding multiple concepts from the same problem is my methodology of teaching. I encourage the students to solve the previous yearโs problems from different competitive exams and tutorial sheets. Students should solve relevant unsolved problems from good test books**ย **

Broadly, I cover the following topics during my course

References:

- a) Classical Mechanics by Herbertย Goldstein
- b) Mechanics by L.D. Landeau and E.M. Lifshitz
- c) Nonlinear Dynamics and Chaos by STROGATZ
- d) Special Theory of Relativity by Robert Resnick
- e) Mechanics by kleppner and kolenkow

I encourage students to solve problems by understanding the basic concepts and applying the first principle to them.

I like to teach classical mechanics and Quantum Mechanics at the Graduate and Post Graduate level.

My approach towards Teaching

**Quantum Mechanics**

David Bohm, in his book โQuantum Theoryโ, discusses three main conceptual differences between Classical and Quantum mechanics:

1) The classical concept of continuous and precisely defined trajectory is fundamentally altered by introducing the description of motion in terms of a series of indivisible transitions.

2) The rigid determinism of classical theory is replaced by the concept of causality as an approximate and statistical trend.

3) Classical assumption that elementary particles have an โintrinsicโ nature that can never change is replaced by the assumption of Wave particle duality: depends on how they are treated by surrounding environment.

As a student of Physics, I like to give special thanks to my teacher โ**Prof. Akhilesh Pandayโ** who taught us mathematical physics, Quantum mechanics, and Nonlinear dynamics during my MSc at JNU. As a QM teacher I keep on evolving my methods to deliver lectures best suited to the students. I draw my inspiration from the course work during MSc, Video lectures of NPTEL **by Prof. V. Balakrishnan** and MIT open course by **Prof. Barton Zwiebach.**

I face two primary challenges regarding the understanding of the subject:

1) It is challenging to justify the existence of Wave-particle duality, Uncertainty principle, and Quantization of energy. This property of nature dominated at the microscopic level, shaded away from the intuition-based analysis of classical mechanics.

Thanks to God, we have beautiful experiments to discuss photoelectric effect, Compton effect, Davisson Germer effect, Youngsโ double slit experiment, and Stern Gerlach experiment. After the discussion of these experiments, students raise logical analogy towards the subject which otherwise is vague and abstract.

2) The abstractness of the mathematical formulation of Quantum mechanics, mainly in Dirac notation and Hilbert space, is another important challenge.

My priority is to make student equipped in mathematical tools of QM so that they can understand the postulates clearly. I also teach Classical mechanics. I always try to draw a mathematical and physical analogy between classical and quantum approaches. I love to use the mathematical formulation of classical mechanics and probability as my support system for Quantum arguments.

Once my students are equipped with mathematical postulates, I apply these postulates to one-dimension free particle, one-dimension infinite, and finite box problems. The Quantum mechanical discussion on Dirac delta potential and the Harmonic oscillator make students confident towards the subject.

Once students prepare themselves for the one-dimensional system, we sail in a new ocean of two- and three-dimension systems. Here we also discuss โspace quantizationโ through Angular momentum Algebra, the understanding of internal symmetry as โSpin โis an exciting part of the subject. Once Schrodinger wave solution of Hydrogen Atom is completed, we discuss Approximation theory like perturbation, Variational method, and WKB approximation. Finally, we cover the theory of scattering and conclude the course with the basics of Relativistic Quantum mechanics.

Thanks to God and Mathematics, they make my life simple as a teacher and Student of Quantum mechanics. Whenever my genius students trap me, I usually save myself by the famous quote of **Feynman **โ**Nobody understands quantum mechanics.****ย **

References:

- Quantum Mechanics by Claude Cohen-Tannoudji
- Quantum Mechanics by R. Shankar
- Quantum Mechanics by D. J. Griffiths
- Quantum Mechanics: concepts and applications / Nouredineย Zettili
- Modern Physics by Arthur and Beiser

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