 Adiabatic approximation in quantum mechanics
 Airy functions and the bouncing electron
 Alpha decay using the WKB approximation
 Angular equation – alternative solution
 Angular momentum: adding 2 spins
 Angular momentum: adding 3 spins
 Angular momentum: adding spins in arbitrary directions
 Angular momentum: addition and ClebschGordan coefficients
 Angular momentum – commutators
 Angular momentum commutators in hydrogen
 Angular momentum – commutators with position and momentum
 Angular momentum: commutators of added spins
 Angular momentum – eigenfunctions
 Angular momentum – eigenvalues
 Angular momentum as a generator of rotations
 Angular momentum – raising and lowering operators
 Angular momentum: restriction to integer values
 Angular momentum and torque
 Antihermitian operators
 Atomic wavefunctions: symmetrization
 Band structure of solids: degeneracy of states
 Band structure of solids: numerical solution
 Band structure of solids: negative energies
 Berry’s phase: definition and value for a spin1 particle in a magnetic field
 Blackbody radiation
 Bosons in the infinite square well
 Buffon’s needle: estimating pi
 Bulk modulus in the electron gas model
 ClebschGordan coefficients for higher spin
 Commutators: a few theorems
 Complex exponentials and trig functions
 Degeneracy pressure in a solid
 Degenerate eigenvalues and GramSchmidt orthogonalization
 Degenerate perturbation theory: two states
 Degenerate perturbation in 3 state system
 Degenerate solutions don’t exist in one dimension
 Deltafunction well – bound state
 Delta function well: bound state – uncertainty principle
 Deltafunction well – scattering
 Delta function potential – moving delta function
 Delta function well as limit of finite square well
 Delta function – Fourier transform
 Delta function in time perturbation
 Determinate states
 Dirac delta function
 Dirac delta function in three dimensions
 Dirac delta function – simple examples
 Double delta function well
 Double delta function well – scattering states
 Dysprosium electron configuration
 EarthSun system as a quantum atom
 Electrodynamics in quantum mechanics: gauge transformations
 Electromagnetic force law in quantum mechanics
 Electromagnetism in quantum mechanics: example
 Electron as a classical spinning sphere
 Electron gas: a crude model of a solid
 Electron gas in a 2d infinite square well
 Electron in a precessing magnetic field
 Electron pressure in a neutron star
 Electron pressure in a white dwarf star
 Energy states: bound and scattering states
 Energy & wave functions: a few theorems
 Energytime uncertainty relation
 Energytime uncertainty: an alternative definition
 Energytime uncertainty principle – example
 Energytime uncertainty principle: Gaussian free particle
 Energytime uncertainty principle: infinite square well
 Exchange force: harmonic oscillator
 Exchange force: infinite square well
 Extended uncertainty principle
 Fermions and bosons: counting states
 Fermions and bosons: nparticle systems
 FeynmanHellmann theorem and the harmonic oscillator
 FeynmanHellmann theorem: hydrogen atom mean values
 Fine structure constant
 Fine structure of hydrogen: Dirac formula
 Fine structure of hydrogen: relativistic correction
 Fine structure of hydrogen: spinorbit coupling
 Fine structure of hydrogen: spinorbit eigenstates and final formula
 Fine structure of a spectral line in hydrogen
 Finite drop potential
 Finite spherical well
 Finite square barrier – scattering
 Finite square well: bound states & even wave functions
 Finite square well: bound states & odd wave functions
 Finite square well – normalization
 Finite square well – numerical solution
 Finite square well – scattering
 Finite step potential – scattering
 First order nondegenerate perturbation theory
 Forbidden transitions in the harmonic oscillator and hydrogen
 The free particle
 Free particle in momentum space
 The free particle as a wave packet
 Free particle: Gaussian wave packet
 Free particle – travelling wave packet
 The free particle: probability current
 Fusion with a muondeuteron system
 Geometric phase is always zero for real wave functions
 Halfharmonic oscillator
 Half life of a beer can
 Hamiltonian matrix elements
 Hamiltonian in twolevel system
 Hamiltonian for threestate system
 Hamiltonian and observables in threestate system
 Harmonic oscillator: algebraic solution; raising and lowering operators
 Harmonic oscillator: algebraic normalization
 Harmonic oscillator – asymptotic solution
 Harmonic oscillator – change in spring constant
 Harmonic oscillator: coherent states
 Harmonic oscillator in an electric field
 Harmonic oscillator – probability of being outside classical region
 Harmonic oscillator ground state – numerical solution
 Harmonic oscillator excited states – numerical solution
 Harmonic oscillator: first order perturbation
 Harmonic oscillator – Hermite polynomials
 Harmonic oscillator: matrix elements
 Harmonic oscillator – mixed initial state
 Harmonic oscillator: mixture of two lowest states
 Harmonic oscillator – position, momentum and energy
 Harmonic oscillator – raising and lowering operator calculations
 Harmonic oscillator: relativistic correction
 Harmonic oscillator: Schrödinger’s exact solution
 Harmonic oscillator – example starting state
 Harmonic oscillator – series solution
 Harmonic oscillator – summary
 Harmonic oscillator – three lowest stationary states
 Harmonic oscillator in 3d – rectangular coordinates
 Harmonic oscillator in 3d: spherical coordinates
 Helium atom
 Helium atom: electronelectron interaction
 Helium atom: parahelium and orthohelium
 Helium atom using the variational principle
 Hermite polynomials – recursion relations
 Hermite polynomials – generation
 Hermite polynomials – the Rodrigues formula
 Hermitian conjugate of an operator
 Hermitian operators
 Hermitian operators: common eigenfunctions implies they commute
 Hermitian operators – equivalence of conditions
 Hermitian operators – a few theorems
 Hermitian operators: periodic function
 Hilbert space – power functions
 Hund’s rules
 Hybrid infinitefinite square well
 Hydrogen atom: coincident spectral lines
 Hydrogen atom: combined position and spin state
 Hydrogen atom in a crystal lattice
 Hydrogen atom – Laguerre polynomials example
 Hydrogen atom – mean radius of electron position
 Hydrogen atom – mixed initial state and mean potential energy
 Hydrogen atom – most probable distance of electron
 Hydrogen atom: powers of the momentum operator
 Hydrogen atom: probability of finding electron inside the nucleus
 Hydrogen atom radial equation
 Hydrogen atom – radial function examples
 Hydrogen atom: radial functions for large l
 Hydrogen atom – series solution and Bohr energy levels
 Hydrogen atom – spectrum
 Hydrogen atom – wave function example 1
 Hydrogen atom – complete wave function & example 2
 Hydrogen atom: wave function example 3
 Hydrogenlike atoms
 Hydrogen molecule ion
 Hydrogen molecule ion – different trial function
 Hydrogen molecule ion – oscillation of the protons
 Hyperfine splitting and the 21 cm line of hydrogen
 Hyperfine splitting in deuterium
 Identical particles: fermions and bosons
 Infinite spherical well – numerical solutions
 Infinite spherical well – spherical Bessel functions
 The infinite square well (particle in a box)
 Infinite square well – average energy
 Infinite square well – centered coordinates
 Infinite square well – change in well size
 Infinite square well – combination of two lowest states
 Infinite square well – cubic sine initial state
 Infinite square well – minimum energy
 Infinite square well: momentum
 Infinite square well: momentum space wave functions
 Infinite square well – numerical solution
 Infinite square well – particle in left half
 Infinite square well – phase difference
 Infinite square well in three dimensions
 Infinite square well – triangular initial state
 Infinite square well with triangular initial state using delta function
 Infinite square well: 2 particle systems
 Infinite square well – uncertainty principle
 Infinite square well with delta function barrier
 Kramers’s relation for averages of radial powers in hydrogen
 Kramers’s relation: application to hydrogen mean values
 Laguerre polynomials – normalization
 Legendre polynomials: generation by GramSchmidt process
 Magnetic resonance
 Matrix elements: example
 Momentum: eigenvalues and normalization
 Momentum space representation of finite wave function
 Momentum space: harmonic oscillator
 Momentum space: mean position
 Momentum space: another example
 Momentum space in 3d
 The need for quantum theory
 Particle on a circular wire
 Periodic potentials: Bloch’s theorem and the band structure of solids
 Periodic table
 Perturbation due to finite size of the proton in hydrogen
 Perturbation theory for higherlevel degenerate systems
 Perturbation theory and the variational principle
 Perturbing the 3d harmonic oscillator
 Perturbation of 3d square well
 Perturbing a particle on a circular wire
 Perturbing the wave function (Stark effect and proton electric dipole moment)
 Phases in the adiabatic approximation
 Phases in the adiabatic theorem: delta function well
 Plancherel’s theorem
 Position and momentum
 Position operator: eigenfunctions
 Probability current
 Probability current in 3d
 Projection operators
 Quantum dots
 Quantum revival time
 Reflectionless potential
 Rigid rotor in quantum mechanics
 Rubber band helium
 Rutherford scattering
 Scattering matrix
 The Schrödinger equation
 The Schrödinger equation: the motivation
 Schrödinger equation – a few theorems
 Schrödinger equation – minimum energy
 Schrödinger equation in three dimensions – spherical harmonics
 Schrödinger equation in three dimensions – radial equation
 Schrödinger equation for 2 particles – separation of variables
 Second order nondegenerate perturbation theory
 Selection rules for spontaneous emission of radiation
 Selection rules in spontaneous emission: transition between spherically symmetric states not allowed
 Selfadjoint differential equations
 Sequential measurements
 Sinusoidal perturbations in time
 Spectral decomposition of operators
 Spherical harmonics – examples
 Spherical harmonics – more examples
 Spherical harmonics: normalization
 Spherical harmonic at the top of the ladder
 Spherical harmonic using the raising operator
 Spin – expectation values of components
 Spin – introduction
 Spin ½
 Spin 1/2 along an arbitrary direction
 Spin 1/2: minimum uncertainty
 Spin 1/2 particle in a magnetic field
 Spin 1/2 particle in timevarying magnetic field
 Spin 1/2: spin components
 Spin 1
 Spin 3/2
 Spin matrices: general case
 Spin and quarks
 Spin – statistical calculations
 Spin: the y component
 Spontaneous emission: Einstein’s argument
 Spontaneous emission rates for the hydrogen atom
 Spontaneous emission rates for hydrogen: general solution
 Spontaneous emission from n=3 to n=1 in hydrogen
 Spontaneous emission from the zero point field
 Stark effect in hydrogen for n = 1 and n = 2
 Stark effect in hydrogen for n = 3; hydrogen wave functions in Maple
 Stark effect: tunnelling probability
 Statistical mechanics in quantum theory: 3d harmonic oscillator
 Statistical mechanics in quantum theory: Bose condensation
 Statistical mechanics in quantum theory: counting states
 Statistical mechanics in quantum theory: counting boson states
 Statistical mechanics in quantum theory: counting states, general case
 Statistical mechanics in quantum theory: energy probabilities
 Statistical mechanics in quantum theory: most probable state
 Statistical mechanics in quantum theory: most probable state for fermions
 StefanBoltzmann law
 Stimulated emission of radiation: lasers
 Stimulated emission of radiation at high frequencies
 Timedependent perturbation theory: iterative solution
 Timedependent perturbation theory: general twostate solution
 Timedependent perturbation theory: switching a perturbation on and off
 Timedependent perturbation theory for a multilevel system
 Timedependent perturbation theory: transition probabilities in a multistate system
 Timedependent perturbation uniform in space
 Timedependent perturbation of the infinite square well
 Time dependent Schrödinger equation: twostate systems
 Timedependent Schrödinger equation: switching a perturbation on and off
 The timeindependent Schrödinger equation
 The timeindependent Schrödinger equation – general solutions
 Transfer matrix
 Translations in space and time
 Uncertainty principle
 Uncertainty principle – examples
 Uncertainty principle: condition for minimum uncertainty
 Uncertainty principle: rates of change of operators
 Uncertainty principle in three dimensions
 Van der Waals interaction
 The variational principle in quantum mechanics
 Variational principle and the delta function well
 Variational principle and the electron in a magnetic field
 Variational principle and the first excited state
 Variational principle and the harmonic oscillator
 Variational principle and the harmonic oscillator – 2
 Variational principle and harmonic oscillator: a more general trial function
 Variational principle and the hydrogen atom
 Variational principle and the hydrogen ion: two parameters
 Variational principle with a twostate hamiltonian
 Variational principle and the Yukawa potential
 Vector spaces and Hilbert space
 Vibrational states in a diatomic molecule (HCl)
 Virial theorem
 Virial theorem in 3d
 WKB approximation
 WKB approximation – alternative derivation
 WKB approximation – analysis of the overlap region near a turning point
 WKB approximation for a barrier with sloping sides
 WKB approximation of a double potential well: turning points
 WKB approximation of doublewell potential: wave functions
 WKB approximation of the harmonic oscillator
 WKB approximation and the hydrogen atom
 WKB approximation and the power law potential
 WKB approximation and the radial equation
 WKB approximation and the reflectionless potential
 WKB approximation: tunneling
 WKB approximation: turning points
 WKB approximation at a turning point with decreasing potential
 The wave function as a probability
 The wave function: Born’s conditions
 The wave function: making energy measurements
 Waveparticle duality
 Zeeman effect: degenerate perturbation theory for n = 2
 Zeeman effect for n = 3: general case
 Zeeman effect for n = 3: strong field
 Zeeman effect for n = 3; weak field
 Zeeman effect for l=0
 Zeeman effect: the n=2 line in hydrogen
 Zeeman effect: strength of magnetic field
 Zeeman effect: strong field
 Zeeman effect: weak field

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Comments
I am going through a QM course and not having an easy time of it. Thanks for putting so much effort into this blog, Its much more comprehensive that many.
Cheers from BC :)
I’m new here and I like your stuff. However, some of your blogs are sequential, but the index is alphabetic. It would be nice if under a topic, say harmonic oscillator, the subtopics were listed sequentially. Or maybe related blogs grouped into chapters.
There are already various ways you can get posts related to a given topic. Use the ‘Search’ box in the left panel, or on the index page use your browser’s search option (Control+F on Windows). The problem indexes for the various textbooks I’m working through provide a grouping of posts into chapters. I’ve also tried to tag each post with relevant keywords, so you can do a tag search.
Links to articles referenced in a post are to be found within that post so it shouldn’t be too hard to find a sequence.