Online quantum mechanics lectures

A complete set of lectures on quantum mechanics by David Miller is available as online videos through links below. Links to slide copies, frequently-asked questions (FAQs), typographical corrections, and some supplementary information are also given.

The material is nominally organized into lectures, with an overall length typical for a lecture in a college course. These are generally also broken up into smaller parts for easier viewing.

This is also the lecture material for a sequence of two online quantum mechanics classes. See this page for more information. Lectures 1 – 26 are from the first of these classes, and lectures 27 – 52 are from the second class.

The lecture material is self-contained, but the lectures closely follow the presentation in the book Quantum Mechanics for Scientists and Engineers (Cambridge) by D. A. B. Miller (“QMSE” for short in this page). Textbook references are given for each lecture portion, and additional material and expanded discussions are also given in this book.

Lecture 1 Introduction to quantum mechanics

Lecture 1a – Introduction to quantum mechanics QMSE 1.1

Lecture 1b – Light QMSE 1.1

Lecture 1c – Matter QMSE 1.1

Lecture 1d – The usefulness of quantum mechanics QMSE 1.1

Lecture 1e – Science, philosophy and meaning QMSE 1.2 – 1.3

Lecture 1 slides

Lecture 2 Classical mechanics, oscillations and waves

Lecture 2a – Useful ideas from classical physics QMSE Appendix B

Lecture 2b – Elementary classical mechanics QMSE B.1

Lecture 2c – Oscillations QMSE B.3

Lecture 2d – The classical wave equation QMSE B.4

Lecture 2 slides

FAQs for lectures 1 and 2

Lecture 3 Wave propagation

Lecture 3a – Plane waves and interference QMSE B.4

Lecture 3b – Diffraction QMSE B.4

Lecture 3c – Diffraction from periodic structures QMSE B.4

Lecture 3 slides

Lecture 4 Schroedinger’s wave equation

Lecture 4a – Schroedinger wave equation introduction QMSE Chapter 2 introduction

Lecture 4b – From de Broglie to Schroedinger QMSE 2.1 – 2.2

Lecture 4c – Diffraction by two slits QMSE 2.3 (first part)

Lecture 4 slides

Lecture 5 Particle in a box

Lecture 5a – Introduction to the particle in a box QMSE 2.6 (first part)

Lecture 5b – Linearity and normalization QMSE 2.4 – 2.5

Lecture 5c – Solving for the particle in a box QMSE 2.6 (first part)

Lecture 5d – Nature of the particle-in-a-box solutions QMSE 2.6 (second part)

Lecture 5 slides

FAQs for lectures 3 – 5

Lecture 6 Particles and barriers

Lecture 6a – Sets of functions QMSE 2.7 (“Completeness of sets – Fourier series”)

Lecture 6b – Orthogonality of functions QMSE 2.7 (“Orthogonality of eigenfunctions” and “Expansion coefficients”)

Lecture 6c – Barriers and boundary conditions QMSE 2.8

Lecture 6 slides

Lecture 7 Finite well and harmonic oscillator

Lecture 7a – Particles in potential wells – introduction QMSE 2.9

Lecture 7b – The finite potential well QMSE 2.9

Lecture 7c – The harmonic oscillator QMSE 2.10

Lecture 7 slides

Lecture 8 The time-dependent Schrödinger equation

Lecture 8a – Introduction to the time-dependent Schrödinger equation QMSE Chapter 3 introduction

Lecture 8b – Rationalizing the time-dependent Schrödinger equation QMSE 3.1 – 3.2

Lecture 8c – Solutions of the time-dependent Schrödinger equation QMSE 3.3

Lecture 8d – Linear superposition QMSE 3.4 – 3.5

Lecture 8 slides

FAQs for lectures 6 – 8

Lecture 9 Time evolution of superpositions

Lecture 9a – Introduction to time evolution of superpositions QMSE 3.5 – 3.6

Lecture 9b – Superposition for the particle in a box QMSE 3.6 (“Simple linear superposition in an infinite potential well”)

Lecture 9c – Superposition for the harmonic oscillator QMSE 3.6 (“Harmonic oscillator example”)

Lecture 9d – The coherent state QMSE 3.6 (“Coherent state”)

Lecture 9 slides

Lecture 10 Wavepackets

Lecture 10a – Introduction to wavepackets QMSE 3.7 introduction

Lecture 10b – Group velocity QMSE 3.7 (“Group velocity” first part)

Lecture 10c – Group velocity for a free electron QMSE 3.7 (“Group velocity” second part)

Lecture 10d – Electron wavepackets QMSE 3.7 (“Examples of motion of wavepackets”)

Lecture 10 slides

Lecture 11 Measurement and expectation values

Lecture 11a – Quantum-mechanical measurement QMSE 3.8

Lecture 11b – Expectation values and operators QMSE 3.9 – 3.10

Lecture 11c – Time evolution and the Hamiltonian QMSE 3.11

Lecture 11 slides

FAQs for lectures 9 – 11

Lecture 12 Uncertainty principle and particle current

Lecture 12a – Momentum, position, and the uncertainty principle QMSE 3.12 – 3.13

Lecture 12b – Particle Current QMSE 3.14

Lecture 12 slides

Lecture 13 Functions and Dirac notation

Lecture 13a – Introduction to functions and Dirac notation QMSE Chapter 4 introduction

Lecture 13b – Functions as vectors QMSE 4.1 (up to “Dirac bra-ket notation”)

Lecture 13c – Dirac notation QMSE 4.1 (first part of “Dirac bra-ket notation”)

Lecture 13d – Using Dirac notation QMSE 4.1 (remainder of 4.1)

Lecture 13 slides

Lecture 14 Vector spaces, operators and matrices

Lecture 14a – Vector space QMSE 4.2

Lecture 14b – Operators QMSE 4.3 – 4.4

Lecture 14c – Linear operators and their algebra QMSE 4.4 – 4.5

Lecture 14 slides

FAQs and typo, lectures 12 – 14

Lecture 15 Types of linear operators

Lecture 15a – Bilinear expansion of operators QMSE 4.6

Lecture 15b – The identity operator QMSE 4.8

Lecture 15c – Inverse and unitary operators QMSE 4.9 – 4.10 (up to “Changing the representation of vectors”)

Lecture 15 slides

Lecture 16 Unitary and Hermitian operators

Lecture 16a – Using unitary operators QMSE 4.10 (starting from “Changing the representation of vectors”)

Lecture 16b – Hermitian operators QMSE 4.11

Lecture 16c – Matrix form of derivative operators QMSE 4.12 – 4.13

Lecture 16 slides

Lecture 17 Operators and quantum mechanics

Lecture 17a – Hermitian operators in quantum mechanics QMSE 5.1

Lecture 17b – General form of the uncertainty principle QMSE 5.2 (up to “Position-momentum uncertainty principle”)

Lecture 17c – Specific uncertainty principles QMSE 5.2 (starting from “Position-momentum uncertainty principle”)

Lecture 17 slides

FAQs, lectures 15 – 17

Lecture 18 Angular momentum

Lecture 18a – Angular momentum operators QMSE Chapter 9 introduction and Section 9.1 (first part)

Lecture 18b – Angular momentum eigenfunctions QMSE 9.1 (remainder)

Lecture 18 slides

Lecture 19 The L squared operator

Lecture 19a – Separating the L squared operator QMSE 9.2

Lecture 19b – Visualizing spherical harmonics QMSE 9.3

Lecture 19c – Notations for spherical harmonics QMSE 9.4

Lecture 19 slides

Lecture 20 The hydrogen atom

Lecture 20a – Multiple particle wavefunctions QMSE Chapter 10 introduction and Section 10.1

Lecture 20b – Solving the hydrogen atom problem QMSE 10.2 – 10.3 (up to “Bohr radius and Rydberg energy”)

Lecture 20c – Informal solution for the relative motion QMSE 10.3 (“Bohr radius and Rydberg energy”)

Lecture 20 slides

FAQs and typos, lectures 18 – 20

Lecture 21 The hydrogen atom solutions

Lecture 21a – Separating for the radial equation QMSE 10.4 (up to “Solution of the hydrogen radial wavefunction”)

Lecture 21b – Radial equation solutions QMSE 10.4 starting with “Solution of the hydrogen radial wavefunction”, and 10.5

Note: Section 10.4 contains the complete mathematical details for solving the radial equation in the hydrogen atom problem. In this sequence of lectures, not all those details are required and they are consequently not all covered in these online lectures, so the additional detail, in particular on power series solutions in section Section 10.4, is optional.

Lecture 21 slides

Lecture 22 Approximation methods

Lecture 22a – Approximation methods – introduction QMSE Chapter 6 introduction

Lecture 22b – Potential well with field QMSE 6.1

Lecture 22c – Use of finite matrices QMSE 6.2

Lecture 22 slides

Lecture 23 Perturbation theory

Lecture 23a – Constructing perturbation theory QMSE 6.3 (up to “First order perturbation theory”)

Lecture 23b – First and second order theories QMSE 6.3 (starting at “First order perturbation theory” up to “Example of well with field”)

Lecture 23c – Applying perturbation theory QMSE 6.3 (starting at “Example of well with field”)

Lecture 23 slides

FAQs and typos, lectures 21-23

Lecture 24 Tight binding and variational models

Lecture 24a – Tight binding model QMSE 6.5

Lecture 24b – The variational method QMSE 6.6

Lecture 24 slides

Lecture 25 Time-dependent perturbation theory

Lecture 25a – Time-dependent perturbation basics QMSE 7.1

Lecture 25b – Simple oscillating perturbations QMSE 7.2 (first part)

Lecture 25c – Transition probabilities QMSE 7.2 (second part)

Lecture 25 slides

Lecture 26 Applying time-dependent perturbation theory

Lecture 26a – Fermi’s Golden Rule QMSE 7.2 (third part)

Lecture 26b – Refractive index QMSE 7.3

Lecture 26 slides

FAQs, lectures 24 – 26

Lecture 27 Quantum mechanics in crystals

Lecture 27a – Introduction to quantum mechanics in crystals QMSE Chapter 8 Introduction

Lecture 27b – Crystal structures QMSE 8.1

Lecture 27 slides

Lecture 28 The Bloch theorem

Lecture 28a – Periodic boundary conditions QMSE 8.2 – 8.3 (through Eq. 8.6)

Lecture 28b – Bloch theorem derivation QMSE 8.3 (from Eq. 8.7)

Lecture 28c – Density of states in k-space QMSE 8.4

Lecture 28 slides

FAQs and typos, lectures 27-28

Lecture 29 Band structures

Lecture 29a – Band structures QMSE 8.5 introduction

Lecture 29b – Band structure diagrams QMSE 8.5

Lecture 29c – Semiconductors, insulators and metals QMSE 8.5

Lecture 29d – Band structures in 3D QMSE 8.5

Lecture 29 slides

Lecture 30 Effective mass theory

Lecture 30a – Effective mass approximation QMSE 8.6 (up to ~ Eq. 8.29)

Lecture 30b – Wavepackets and effective mass theory QMSE 8.6 (from ~ Eq. 8.29 to “Effective mass approximation …” subsection)

Lecture 30c – Semiconductor heterostructures QMSE 8.6 (“Effective mass approximation …” subsection)

Lecture 30 slides

Lecture 31 Density of states

Lecture 31a – Energy density of states in bulk crystals QMSE 8.7

Lecture 31b – Quantum wells QMSE 8.8 through end of “Formal separation …” subsection

Lecture 31c – Density of states in quantum wells QMSE 8.8 from “Quantum well …” subsection

Lecture 31 slides

FAQs and typos, lectures 29 – 31

Lecture 32 Optical absorption in semiconductors

Lecture 32a – Introduction to optical absorption in semiconductors QMSE 8.10 (beginning)

Lecture 32b – Perturbing Hamiltonian QMSE 8.10 through “Form of the perturbing …” (with Appendix E for optional background)

Lecture 32c – Direct transitions QMSE 8.10 subsection “Direct valence …” through paragraph after Eq. 8.98

Lecture 32d – Transitioning from sums to integrals QMSE 5.3

Lecture 32e – Total transition rate QMSE 8.10 subsection “Direct valence …” starting above Eq. 8.99 through Eq. 8.107

Lecture 32f – Absorption coefficient QMSE 8.10 starting just above Eq. 8.108

Lecture 32 slides

Lecture 33 Methods for one-dimensional problems

Lecture 33a – Introduction to methods for one-dimensional problems QMSE Chapter 11 introduction

Lecture 33b – Tunneling currents QMSE 11.1

Lecture 33c – Transfer matrix method QMSE 11.2 up to “Calculation of eigenenergies …”

Lecture 33d – Transfer matrix and bound states QMSE 11.2 from “Calculation of eigenenergies …”

Lecture 34 Electron spin

Lecture 34a – Introduction to electron spin QMSE Chapter 12 introduction

Lecture 34b – Angular momentum and magnetic moments QMSE 12.1

Lecture 34c – Spin angular momentum QMSE 12.2

Lecture 34d – Operators for spin angular momentum QMSE 12.3

Lecture 34 slides

Lecture 35 Spin states

Lecture 35a – Visualizing spin states QMSE 12.4

Lecture 35b – Wavefunctions, spin and Hilbert space QMSE 12.5

Lecture 35c – The Pauli equation QMSE 12.6

Lecture 35d – Where does spin come from? QMSE 12.7

Lecture 35 slides

Lecture 36 Identical particles and exchange

Lecture 36a – Scattering identical particles QMSE 13.1 up to Eq. 13.17

Lecture 36b – Fermions and bosons QMSE 13.1 last 4 paragraphs, and 13.2

Lecture 36c – States, single-particle states, and modes QMSE 13.3

Lecture 36d – Exchange energy QMSE 13.4

Lecture 36 slides

FAQs and typos, lectures 34 – 36

Lecture 37 States of identical particles

Lecture 37a – Multiple particle states QMSE 13.5

Lecture 37b – Multiple particle basis functions QMSE 13.6 up to Eq. 13.50

Lecture 37c – Numbers of states QMSE 13.6 subsection “Example numbers of states”

Lecture 37d – Analogy for counting states QMSE 13.6 subsection “Bank account analogy for counting states”

Lecture 37 slides

Lecture 38 Multiple particle distributions

Lecture 38a – Thermal distributions QMSE 13.7

Lecture 38b – Examples of states of multiple identical particles QMSE 13.8

Lecture 38c – Quantum mechanical particles reconsidered QMSE 13.9 – 13.10

Lecture 38 slides

Lecture 39 Operators for harmonic oscillators

Lecture 39a – Raising and lowering operators QMSE 15.1 up to Eq. 15.16

Lecture 39b – Properties of raising and lower operators QMSE 15.1 from “Properties of raising …”

Lecture 39c – Hamilton’s equations QMSE 15.2

Lecture 39 slides

(No FAQs for lectures 37 – 39)

Lecture 40 Quantizing the electromagnetic field

Lecture 40a – Field modes as oscillators QMSE 15.3 subsection “Description of a mode …”

Lecture 40b – Electromagnetic mode Hamiltonian QMSE 15.3 from subsection “Hamiltonian for …” to the paragraph after Eq. 15.64

Lecture 40c – Quantum states of an electromagnetic mode QMSE 15.3 from two paragraphs above Eq. 15.65 to end of 15.4

Lecture 40d – Field operators QMSE 15.5

Lecture 40 slides

Lecture 41 Quantum states of the electromagnetic field

Lecture 41a – Number states QMSE 15.6 to end of subsection “Representation of time dependence …”

Lecture 41b – The coherent state QMSE 15.6 subsection “Coherent state”

Lecture 41c – Sets of modes QMSE 15.7 to start of “Multimode photon states”

Lecture 41d – Multimode photon states QMSE 15.7 subsection “Multimode photon states”

Lecture 41e – Multimode operators QMSE 15.7 subsection “Commutation relations … ” to end

Lecture 41 slides

Lecture 42 Fermion annihilation and creation operators

Lecture 42a – Describing fermion states QMSE Chapter 16 introduction and Section 16.1 up to beginning of “Fermion creation operators”

Lecture 42b – Creation operators QMSE 16.1 subsection “Fermion creation operators”

Lecture 42c – Annihilation operators QMSE 16.1 subsection “Fermion annihilation operators”

Lecture 42d – Mixtures of creation and annihilation operators QMSE 16.1 subsection “Mixtures of creation and annihilation operators”

Lecture 42 slides

FAQs and typos, lectures 40 – 42

Lecture 43 Fermion wavefunction and Hamiltonian operators

Lecture 43a – Wavefunction operator QMSE 16.2

Lecture 43b – Representing fermion Hamiltonians QMSE 16.3 up to paragraph after Eq. 16.56

Lecture 43c – Fermion Hamiltonians with multiple particle states QMSE 16.3 subsection “Single particle fermion Hamiltonians with multiple particle states”

Lecture 43 slides

Lecture 44 Fermion operators and multiple particles

Lecture 44a – Single-particle fermion operators QMSE 16.3 subsection “Representation of general single-particle fermion operators”

Lecture 44b – Two-particle fermion operators QMSE 16.3 subsection “Two-particle fermion operators”

Lecture 44 slides

Lecture 45 Interaction of different particles

Lecture 45a – States with different kinds of particles QMSE 17.1

Lecture 45b – Electron – photon interaction QMSE 17.2

Lecture 45c – Rewriting perturbation theory QMSE 17.3

Lecture 45d – Photon absorption QMSE 17.4 through end of subsection “Absorption”

Lecture 45 slides

FAQs and typo, lectures 43 – 45

Lecture 46 Spontaneous and stimulated emission

Lecture 46a – Spontaneous emission QMSE 17.4 subsection “Spontaneous emission”

Lecture 46b – Stimulated emission QMSE 17.4 subsections “Stimulated emission” and “Multiple-photon case”

Lecture 46c – Total spontaneous emission rate QMSE 17.4 subsection “Total spontaneous emission rate”

Lecture 46 slides

Lecture 47 Mixed states and the density matrix

Lecture 47a – Introduction to mixed states and the density matrix QMSE Chapter 14 introduction

Lecture 47b – Pure and mixed states QMSE 14.1 (first part)

Lecture 47c – Mixed states with potential wells QMSE 14.1 (second part)

Lecture 47d – Representing mixed states QMSE 14.2 and 14.3 through Eq. 14.8

Lecture 47e – Properties of the density matrix QMSE 14.3 (remainder)

Lecture 47f – Time-evolution of the density matrix QMSE 14.4

Lecture 47 slides

Lecture 48 The density matrix and optical absorption

Lecture 48a – Induced dipole and a two-level system QMSE 14.5 through Eq. 14.35

Lecture 48b – Behavior of the density matrix in time QMSE 14.5 from Eq. 14.35 through the paragraph after Eq. 14.40

Lecture 48c – Behavior with oscillating field QMSE 14.5 from paragraph above Eq. 14.41 through Fig. 14.1

Lecture 48d – Density matrix and nonlinear optics QMSE 14.5 after Fig. 14.1, and 14.6

Lecture 48 slides

FAQs and typos, lectures 46 – 48

Lecture 49 Quantum measurements and encryption

Lecture 49a – Representing information QMSE Chapter 18 introduction

Lecture 49b – Collapse and the no-cloning theorem QMSE 18.1 and 18.2 through “No cloning theorem” subsection

Lecture 49c – Quantum cryptography QMSE 18.2 subsection “A simple quantum encryption scheme”