Quantum optics studies light using quantum states of the electromagnetic field and their interaction with matter. Photon statistics asks how detections fluctuate; the quantum theory of optical coherence relates those detections to field correlations. A coherent state, thermal light, and a Fock state can have the same mean photon number yet different pair counts. This distinction makes photon counting useful for testing sources intended to emit one photon at a time.

An effective generator of evolution over a period of a time-periodic Quantum Hamiltonian, with the choice of quasienergy branch stated.

By Barton Zwiebach, explicitly credited as B. Zwiebach on PDF p. 1, dated 4 November 2013. Chapter 6 notes in Quantum Physics II (8.05), Fall 2013, listed for lectures 12–16. Massachusetts Institute of Technology issues the course; MIT OpenCourseWare hosts this authored document.

Online text: ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/79a8091ef4f18d8e3ff76a097e8db33c_MIT8_05F13_Chap_06.pdf

Cited passages: §§2.1–2.2, printed pp. 10–14; §2.3, printed pp. 15–17, equations (2.45), (2.46) and (2.52).

By Richard Fitzpatrick. Page footer dated 22 January 2016; cited equations (7.57), (7.65).

By Richard Fitzpatrick. Page footer dated 22 January 2016; cited §7.6, equations (7.82)–(7.94).

A transition during a sweep through an avoided crossing of energy levels.

For an isolated quantum system, pure states are normalized rays in a complex Hilbert space, observables are self-adjoint operators, and their probabilities obey the Born rule. A spectral projector $P_a$ has outcome probability $⟨\psi |P_a|\psi ⟩$; an ideal repeatable projective measurement has conditional state $P_a\psi /\sqrt{⟨\psi |P_a|\psi ⟩}$. The Schrödinger equation specifies continuous unitary evolution between such ideal measurements, given a Hamiltonian operator. General measurements need not have the projective state-update rule.

Composite systems use the tensor product of their state spaces. Identical particles additionally obey the bosonic or fermionic exchange symmetry appropriate to their species. The photoelectric effect, Davisson–Germer experiment and double-slit experiment motivate energy quanta, matter-wave phases and probability interference, respectively; these experiments constrain the framework but do not separately prove every abstract postulate or specify every system's Hamiltonian.