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Photoelectron spectroscopy measures the kinetic energies of photoelectrons produced by illuminating matter with photons of known energy. The photoelectric effect supplies the emission mechanism; spectroscopy turns the distribution of emitted electron energies into information about occupied energy levels and chemical bonds. A broad survey helps identify chemical elements, while small shifts within one element's lines can distinguish different chemical surroundings. These are different questions: finding carbon does not establish which chemical bonds its chemical atoms form.

The useful inversion is an energy balance. A known incoming photon energy pays for removal of an electron and for its outgoing kinetic energy. To apply that balance to a solid, specify the zero of energy and the work function of the instrument. Photoelectron binding energy reference derives the conversion for a conducting sample in electrical contact with its analyzer. A free molecule instead has an ionization energy referenced to an electron at rest in vacuum; it need not share a Fermi level with the analyzer.

A photon is one quantum of the electromagnetic field. In vacuum it has zero rest mass, energy $E=h\nu =\hslash \omega$, and momentum magnitude $p=E/c$. Its two physical polarization degrees of freedom are transverse to its propagation direction. A monochromatic field mode can contain zero, one or several photons; its photon number distinguishes these quantum states.

The photoelectric effect illustrates a photon's discrete energy exchange: increasing incident frequency increases the available electron kinetic energy, whereas increasing light intensity primarily increases the rate of events in the weak-illumination regime. Compton scattering additionally tests the associated momentum transfer. Interference still depends on probability amplitudes, so describing light in terms of photons does not discard its wave behavior.

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.

An experimental physicist known for measurements of electron charge and the photoelectric effect. The Millikan photoelectric experiment describes the apparatus and stopping-voltage measurements behind his 1916 test.^[ref]