Quantum Mechanics: Foundations to Advanced
A rigorous beginner-to-advanced native quantum mechanics textbook: experiments, complex amplitudes, Born probabilities, wavefunctions, operators, dynamics, measurement, bound states, spin, identical particles, approximation and decoherence. Original derivations and worked problems, with embedded MIT OpenCourseWare lectures and credited scientific diagrams.
Published syllabus
Course Units
Introduction to Quantum Physics: Experiments, States, and Probability
Begin from the physical evidence that classical models fail, learn the indispensable mathematics of amplitudes and measurement, and build an experimentally meaningful model of a two-path quantum system.
Wavefunctions, normalization, and probability current
Construct position-space quantum states from the Born density and normalization, then derive probability flow and the meaning of wavepacket width.
Linear operators, observables, and commutator algebra
Relate experimental questions to Hermitian operators, eigenvalues, basis changes, and commutators without assuming all observables can share definite values.
Time evolution, propagators, and quantum control
Derive unitary time evolution from the Hamiltonian and solve exactly for stationary energies and a two-level example.
Projective measurement, generalized measurements, and uncertainty
Develop projective measurements and generalized instruments from first principles, then distinguish quantum uncertainty, measurement disturbance, and experimental imprecision.
Finite wells, bound states, scattering, and tunneling
Solve confined states and scattering in one dimension using Schrödinger boundary conditions, matching, quantization and conserved probability current.
The harmonic oscillator: wavefunctions and ladder algebra
Derive the oscillator spectrum algebraically, normalize the Fock states, and compare energy eigenstates with coherent superpositions.
Angular momentum, rotations, and spin
Introduce orbital and intrinsic angular momentum as generators of rotations and compute spin-one-half measurements and rotations.
Tensor products and addition of angular momentum
Develop tensor-product spins, total-angular-momentum eigenstates, Clebsch–Gordan coefficients and singlet–triplet physics.
Identical particles, exchange symmetry, and quantum statistics
Construct bosonic and fermionic two-particle states, derive Pauli exclusion and distinguish exchange symmetry from interactions.
Approximation theory: perturbations, WKB, and time-dependent transitions
Derive perturbative energy shifts, explain degenerate-state handling, and compare variational and semiclassical approximations.
Density matrices, decoherence, open dynamics, and quantum foundations
Distinguish empirical quantum predictions from interpretations, derive reduced-state dephasing and assess claims about measurement and emergence of classical behavior.