Quantum Mechanics 1 (MSc)

Overview

In this course, we give an introduction to quantum mechanics.

Broadly, this course covers: introduction to quantum principles, entanglement, quantum mechanical wave function, Born interpretation, basic formalism (Dirac bra-ket formalism), operators and their representation, review of one dimensional examples, one dimensional harmonic oscillator, creation and annihilation operators, angular momentum, spin, symmetries in quantum mechanics, hydrogen atom.

Course prerequisites

• linear algebra
• calculus
• differential equations

Meeting time and location

• Tue, Thu, and Fri, 11:00 am – 11:50 am in Block II LT1 (106)
• Tutorials: Thu 4:00 pm – 4:50 pm and Fri 2:00 pm – 2:50 pm in Block III LT3 (68)

Instructor

• Sarthak Parikh (he/him) · Office hours by appointment
• Teaching assistant: Shivam Burman

Grading

• Final exam: 40% (closed book)
• Mid-term exam: 40% (closed book)
• Presentations: 10% + 10% (two blackboard presentations, open notes, 5 min + 1 min Q&A each)
• Ungraded practice problems discussed during tutorials.

Tentative list of topics

• Introduction, quantum mechanical wave function, Born interpretation (Ch. 1 & 2 of Susskind)
• EPR paradox, entangled states, hidden variables, Bell’s inequality (Ch. 3.9 of Sakurai), GHZM experiment
• QM in Dirac notation, bra-ket algebra, projection operators; matrix representation of vectors and operators (Ch. 1 of Sakurai; Ch. 4 of Shankar)
• Review of one dimensional examples (particle in a box, step potential, Dirac delta function, periodic potential) (Ch. 5 of Shankar; Griffiths)
• 1D harmonic oscillator, creation/annihilation (ladder) operators, number operator and its eigenstates (Ch. 7 of Shankar)
• Quantum mechanics in 2 and 3 dimensions in Cartesian coordinates, separation of variables
• Quantum theory of angular momentum, eigenvalues and eigenfunctions (Ch. 12 of Shankar; Ch. 3 of Sakurai)
• Schrödinger equation in spherical coordinates, free particle and spherically symmetric potentials, hydrogen atom (Ch. 13 of Shankar)
• Quantum theory of spin angular momentum (Ch. 14 of Shankar)
• Identical particles, exchange symmetry, conservation laws and degeneracy, Pauli principle, discrete symmetries (Ch. 11 of Shankar; Ch. 4 & 6 of Sakurai)

References

• R. Shankar, Principles of Quantum Mechanics (2nd ed., Springer, 2006)
• J. J. Sakurai, Modern Quantum Mechanics (2nd ed., Addison-Wesley)
• David J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall)
• L. Susskind, A. Friedman, Quantum Mechanics: The Theoretical Minimum (Basic Books)