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
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.
Construct position-space quantum states from the Born density and normalization, then derive probability flow and the meaning of wavepacket width.
Relate experimental questions to Hermitian operators, eigenvalues, basis changes, and commutators without assuming all observables can share definite values.
Derive unitary time evolution from the Hamiltonian and solve exactly for stationary energies and a two-level example.
Develop projective measurements and generalized instruments from first principles, then distinguish quantum uncertainty, measurement disturbance, and experimental imprecision.
Solve confined states and scattering in one dimension using Schrödinger boundary conditions, matching, quantization and conserved probability current.
Derive the oscillator spectrum algebraically, normalize the Fock states, and compare energy eigenstates with coherent superpositions.
Introduce orbital and intrinsic angular momentum as generators of rotations and compute spin-one-half measurements and rotations.
Develop tensor-product spins, total-angular-momentum eigenstates, Clebsch–Gordan coefficients and singlet–triplet physics.
Construct bosonic and fermionic two-particle states, derive Pauli exclusion and distinguish exchange symmetry from interactions.
Derive perturbative energy shifts, explain degenerate-state handling, and compare variational and semiclassical approximations.
Distinguish empirical quantum predictions from interpretations, derive reduced-state dephasing and assess claims about measurement and emergence of classical behavior.