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A physicist who developed wave mechanics. In 1926, Erwin Schrödinger made the energies of chemical atoms an eigenvalue problem, rather than prescribing a separate quantization rule for each classical orbit. He shared the Nobel Prize in Physics in 1933 with Paul Dirac.^[ref]

The Schrödinger equation turns a proposed Hamiltonian operator into predictions for a wavefunction and its evolution. Boundary conditions can select discrete energy eigenvalues, while quantum superposition makes their relative quantum phases observable through interference. The infinite square well gives a transparent worked example; a hydrogen atom supplies a physical application with a different potential energy.

The Davisson–Germer experiment gives a complementary experimental route into matter waves: an accelerated electron beam scattered from a nickel crystal produces direction-dependent collected electric current. Its apparatus and angular scans make the wave prediction testable. Interpreting a wavefunction as a probability amplitude also requires the Born rule; that statistical interpretation deserves its own history alongside Erwin Schrödinger's dynamics.

Paul Dirac sought a relativistic quantum mechanics whose evolution equation remained first order in both time and spatial derivatives. A free-particle Hamiltonian $H=c\mathbf{\alpha }\cdot \mathbf{p}+\beta m{c}^2$ reproduces the relativistic relation $H^2=c^2{\mathbf{p}}^2+m^2{c}^4$ when its coefficient matrices satisfy suitable anticommutator identities. The required multi-component wave function incorporates electron spin within the relativistic dynamics. His 1928 paper used this construction to address the doubling of atomic states that earlier theories had treated by adding spin separately.^[ref]

A physicist who developed a relativistic theory of the electron. He shared the Nobel Prize in Physics in 1933 with Erwin Schrödinger.^[ref]