Quantum Theory I: Lecture Notes

✍ Scribed by Prof. Senthil Todadri

• Publisher: Massachusetts Institute of Technology (MIT)
• Year: 2017
• Tongue: English
• Leaves: 131
• Series: Quantum Theory 01
• Category: Library

✦ Table of Contents

Sep. 6, 2017
A Weird'' Example in Quantum Mechanics The Fundamental Postulates of Quantum Mechanics Mathematical Preliminaries Hilbert Spaces Sep. 11, 2017 More Relevant Math Inner Products Dual Space Orthonormal Bases Operators Operators as Matrices in a Given Basis Adjoint Operators Operator Examples Eigenstates and Eigenvalues Sep. 13, 2017 Even More Math More on Matrix Representations Unitary Transformations Diagonalization of Hermitian Operators Simultaneous Diagonalization Measurement Comments Spin-12 Systems Sep. 18, 2017 Measurement Spin-12 Systems The Stern–Gerloch Filter Revisited Compatible and Incompatible Observables The Generalized Uncertainty Relation Position and Momentum Sep. 20, 2017 The Position Operator Measurement of Position Hilbert Spaces Generalizing to Particles in Dimension d The Momentum Operator Momentum Basis Normalization of Position and Momentum Eigenstates The Uncertainty Principle Minimum Uncertainty States Momentum and Translation Sep. 25, 2017 Solving Problems in Convenient Bases Quantum Dynamics Brief Aside on Classical Mechanics The Heisenberg Picture Energy Eigenstates Example: Spin Precession In a Magnetic Field Sep. 27, 2017 Spin Precession In a Magnetic Field Schrödinger Picture Heisenberg Picture Particle in a Potential Example: Charged Particle in a Uniform Electric Field Example: Simple Harmonic Oscillator Oct. 2, 2017 General Time Dependent Hamiltonians Interaction Picture Oct. 4, 2017 Spin-12 in an AC Field Resonant Drive Off-Resonant Drive Path Integral Formulation of Quantum Mechanics Oct. 11, 2017 Path Integral Formulation of Quantum Mechanics The Propagator Path Integrals Oct. 16, 2017 Path Integrals Technical Details Oct. 23, 2017 Stationary Phase Approximation Quantum Particles in Electromagnetic fields Constant Potentials Electromagnetic Fields Gauge Invariance in Quantum Mechanics Aharonov–Bohm Effect Oct. 25, 2017 Aharonov–Bohm Effect Magnetic Monopoles Oct. 30, 2017 Magnetic Monopoles QM of a Charged Particle Moving in a Magnetic Monopole Field Charged Particle in a Uniform Magnetic Field Degeneracy Nov. 1, 2017 Charged Particle in a Uniform Magnetic Field Composite Systems Quantum Entanglement Nov. 13, 2017 Symmetries in Quantum Mechanics Symmetry Transformations Continuous Symmetries and Conservation Laws Translations Time Translations Rotations Nov. 15, 2017 Rotations Eigensystem of Angular Momentum Nov. 20, 2017 Matrix Elements of Angular Momentum Operators Rotation Groups Nov. 22, 2017 `39`42`"613A4547"603ASO(3) versus 3942"613A``4547`"603ASU(2)
Addition of Angular Momentum
Discrete Symmetries
Nov. 27, 2017
Parity
Some Standard Terminology
Wavefunctions Under Parity
Momentum and Angular Momentum
Selection Rules
Time Reversal
Time Reversal and Spin
Nov. 29, 2017
Consequences of Time Reversal Symmetry
Spinless Particles
No Conservation Law
Kramer's Rule for Half-Integer Spin
Uses of Symmetry in Solving the Schrödinger Equation
Symmetric Double-Well Potential
3D Particle in a Spherically Symmetric Potential
Approximation Methods
Time-Independent Perturbation Theory
Dec. 4, 2017
Non-degenerate Time-Independent Perturbation Theory
The First-Order Energy Shift
The First-Order Correction to the Eigenstate
The Second-Order Energy Shift
Examples of Time-Independent Perturbation Theory
Spin in a Magnetic Field
The Quadratic Stark effect
Van der Waals Interaction
Dec. 6, 2017
Degenerate Perturbation Theory
Linear Stark Effect
Time-Dependent Perturbation Theory
SHO in a Time-Dependent Electric Field
Second-Order Transition Amplitude
Dec. 11, 2017
Harmonic Perturbations
The Photoelectric Effect

✦ Subjects

quantum mechanics; quantum physics; 8.321