- Angular equation – alternative solution
- Angular momentum: adding 2 spins
- Angular momentum: adding spins in arbitrary directions
- Angular momentum: addition and Clebsch-Gordan 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
- Anti-hermitian operators
- Atomic wavefunctions: symmetrization
- Buffon’s needle: estimating pi
- Clebsch-Gordan coefficients for higher spin
- Commutators: a few theorems
- Complex exponentials and trig functions
- Degenerate eigenvalues and Gram-Schmidt orthogonalization
- Degenerate solutions don’t exist in one dimension
- Delta-function well – bound state
- Delta function well: bound state – uncertainty principle
- Delta-function well – scattering
- Delta function potential – moving delta function
- Delta function well as limit of finite square well
- Delta function – Fourier transform
- 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
- Earth-Sun 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
- Energy states: bound and scattering states
- Energy & wave functions: a few theorems
- Energy-time uncertainty relation
- Energy-time uncertainty: an alternative definition
- Energy-time uncertainty principle – example
- Energy-time uncertainty principle: Gaussian free particle
- Energy-time uncertainty principle: infinite square well
- Exchange force: infinite square well
- Extended uncertainty principle
- Fermions and bosons: n-particle systems
- 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
- 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
- Half-harmonic oscillator
- Hamiltonian matrix elements
- Hamiltonian in two-level system
- Hamiltonian for three-state system
- Hamiltonian and observables in three-state system
- Harmonic oscillator: algebraic solution
- Harmonic oscillator: algebraic normalization
- Harmonic oscillator – asymptotic solution
- Harmonic oscillator – change in spring constant
- Harmonic oscillator: coherent states
- Harmonic oscillator – probability of being outside classical region
- Harmonic oscillator ground state – numerical solution
- Harmonic oscillator excited states – numerical solution
- 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: 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 3-d – rectangular coordinates
- Harmonic oscillator in 3-d: spherical coordinates
- Helium atom
- Helium atom: electron-electron interaction
- Helium atom: parahelium and orthohelium
- 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
- Hybrid infinite-finite square well
- Hydrogen atom: coincident spectral lines
- Hydrogen atom: combined position and spin state
- 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: 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
- Hydrogen atom – spectrum
- Hydrogen atom – wave function example 1
- Hydrogen atom – wave function example 2
- Hydrogen atom: wave function example 3
- Hydrogen-like atoms
- Identical particles
- 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
- Laguerre polynomials – normalization
- Legendre polynomials: generation by Gram-Schmidt process
- 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 3-d
- The need for quantum theory
- Particle on a circular wire
- Plancherel’s theorem
- Position and momentum
- Position operator: eigenfunctions
- Probability current
- Probability current in 3-d
- Projection operators
- Quantum revival time
- Reflectionless potential
- Rigid rotor in quantum mechanics
- 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
- Self-adjoint differential equations
- Sequential measurements
- 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 time-varying 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
- The time-independent Schrödinger equation
- The time-independent 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
- Vector spaces and Hilbert space
- Vibrational states in a diatomic molecule (HCl)
- Virial theorem
- Virial theorem in 3-d
- The wave function as a probability
- The wave function: Born’s conditions
- The wave function: making energy measurements
- Wave-particle duality
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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