Motivations for studying quantum mechanics – Basic principles of quantum mechanics,Probabilities and probability amplitudes – Linear vector spaces , bra and ket vectors – Completeness, orthonormality, basis vectors – Orthogonal, Hermitian and Unitary operators, change of basis.

Eigenvalues and expectation values, position and momentum representation – Measurement and the generalized uncertainty principle – Schrodinger equation, plane wave solution – Probability density and probability current – Wavepackets and their time evolution – Ehrenfest relations – 1-dimensional potential well problems, particle in a box – Tunnelling through a potential barrier – The linear harmonic oscillator; Operator approach – The linear harmonic oscillator and the Hermite polynomials.

Coherent states and their properties. Application to optics – Other interesting superpositions of basis states such as squeezed light – Motion in 3-dimensions; The central potential problem – Orbital angular momnetum and spherical harmonics – Hydrogen atom ; its energy eigenvalues and eigenfunctions – Additional symmetries of the hydrogen atom – The deuteron ; Estimation of the size of the deuteron – The isotropic oscillator, energy degeneracy – Invariance principles and conservation laws – Spin and the Pauli matrices – Addition of angular momentum – The spin-orbit coupling and its consequences.

Charged particle in a uniform magnetic field; Energy eigenvalues and eigenfunctions – The Schrodinger, and Heisenberg pictures, Heisenberg equations of motion – The interaction picture – The density operator; pure and mixed states, with examples – An introduction to perturbation theory; its relevance, and physical examples – Time-independent perturbation theory : non-degenerate case – Time-independent perturbation theory:degenerate case – Time- dependent perturbation theory; atom- field interactions and the dipole approximation – Examples of time-dependent calculations – Summary of non-classical effects surveyed in the course

Other Resources

Course Curriculum

Mod-01 Lec-01 Quantum Mechanics — An Introduction Details 49:33
Mod-01 Lec-02 Linear Vector Spaces – I Details 1:4:15
Mod-01 Lec-03 Linear Vector Spaces – II: The two-level atom Details 47:31
Mod-01 Lec-04 Linear Vector Spaces – III: The three-level atom Details 50:26
Mod-01 Lec-05 Postulates of Quantum Mechanics – I Details 50:50
Mod-01 Lec-06 Postulates of Quantum Mechanics – II Details 52:29
Mod-01 Lec-07 The Uncertainty Principle Details 50:33
Mod-01 Lec-08 The Linear Harmonic Oscillator Details 52:18
Mod-01 Lec-09 Introducing Quantum Optics Details 50:28
Mod-01 Lec-10 An Interesting Quantum Superposition: The Coherent State Details 52:43
Mod-01 Lec-11 The Displacement and Squeezing Operators Details 51:51
Mod-01 Lec-12 Exercises in Finite Dimensional Linear Vector Spaces Details 57:28
Mod-01 Lec-13 Exercises on Angular Momentum Operators and their algebra Details 49:31
Mod-01 Lec-14 Exercises on Quantum Expectation Values Details 50:23
Mod-01 Lec-15 Composite Systems Details 50:9
Mod-01 Lec-16 The Quantum Beam Splitter Details 49:9
Mod-01 Lec-17 Addition of Angular Momenta – I Details 53:54
Mod-01 Lec-18 Addition of Angular Momenta – II Details 50:48
Mod-01 Lec-19 Addition of Angular Momenta – III Details 54:20
Mod-01 Lec-20 Infinite Dimensional Linear Vector Spaces Details 52:31
Mod-01 Lec-21 Square-Integrable Functions Details 47:53
Mod-01 Lec-22 Ingredients of Wave Mechanics Details 50:19
Mod-01 Lec-23 The Schrodinger equation Details 49:5
Mod-01 Lec-24 Wave Mechanics of the Simple Harmonic Oscillator Details 49:18
Mod-01 Lec-25 One-Dimensional Square Well Potential: The Bound State Problem Details 51:7
Mod-01 Lec-26 The Square Well and the Square Potential Barrier Details 56:33
Mod-01 Lec-27 The Particle in a one-dimensional Box Details 47:55
Mod-01 Lec-28 A Charged Particle in a Uniform Magnetic Field Details 54:43
Mod-01 Lec-29 The Wavefunction: Its Single-valuedness and its Phase Details 1:19
Mod-01 Lec-30 The Central Potential Details 56:24
Mod-01 Lec-31 The Spherical Harmonics Details 55:38
Mod-01 Lec-32 Central Potential: The Radial Equation Details 52:36
Mod-01 Lec-33 Illustrative Exercises -I Details 56:37
Mod-01 Lec-34 Illustrative Exercises -II Details 1:24
Mod-01 Lec-35 Ehrenfest’s Theorem Details 56:10
Mod-01 Lec-36 Perturbation Theory – I Details 52:51
Mod-01 Lec-37 Perturbation Theory – II Details 46:16
Mod-01 Lec-38 Perturbation Theory – III Details 47:32
Mod-01 Lec-39 Perturbation Theory – IV Details 55:22
Mod-01 Lec-40 Time-dependent Hamiltonians Details 50:26
Mod-01 Lec-41 The Jaynes-Cummings model Details 52:50

This course is part of NPTEL online courses, delivered by IIT Madras.

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