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The 100 pages that link to Schrödinger equation, each with the reason it gives.

• Relativistic quantum chemistryCompared with: It is the baseline whose missing relativistic effects motivate more complete treatments.

• Bohr modelCompared with: It replaces fixed electron paths with quantum states that explain more complex atoms.

• Wave equationCompared with: Unlike the wave equation, it generally permits instantaneous spreading rather than finite-speed propagation.

• Dirac equationCompared with: Its success for slow particles left the relativistic electron problem unresolved.

• Werner HeisenbergCompared with: It presents quantum dynamics in wave form, complementary to Heisenberg’s matrix formulation.

• Relativistic chemistryCompared with: Its ordinary electronic solutions omit effects captured by relativistic treatments.

• Hamilton–Jacobi equationCompared with: Its semiclassical limit yields an equation closely related to the classical Hamilton–Jacobi equation.

• Matrix mechanicsCompared with: Its wavefunction evolution offers a contrasting representation of quantum dynamics.

• Klein–Gordon equationCompared with: Schrödinger’s familiar equation is first-order in time, unlike this relativistic second-order equation.

• Sommerfeld modelCompared with: Its wave solutions superseded Sommerfeld’s prescribed classical-like electron orbits.

• Feynman–Kac formulaCompared with: After transformations, its imaginary-time form connects to Feynman–Kac expectations.

• Wave function collapseCompared with: Its smooth evolution differs from the discontinuous measurement update called collapse.

• Parabolic partial differential equationCompared with: Its evolution is dispersive and reversible, unlike ordinary diffusive parabolic evolution.

• Relativistic quantum mechanicsCompared with: It works at low speeds but does not satisfy special-relativistic symmetry.