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

• Molecular orbital theoryNarrower topic: Molecular orbitals are approximate solutions to this equation for molecules.

• Molecular orbitalNarrower topic: Molecular orbitals approximate solutions to this equation for electrons in molecules.

• Quantum harmonic oscillatorNarrower topic: The oscillator’s energy levels follow by solving its stationary form.

• Valence bond theoryNarrower topic: Valence bond theory approximates molecular states using solutions built from atomic wavefunctions.

• Computational chemistryNarrower topic: Electronic-structure methods approximate its solutions for atoms and molecules.

• Hartree–Fock methodNarrower topic: Hartree–Fock approximates a many-electron solution to this equation.

• Rydberg formulaNarrower topic: Solving it for a Coulomb-bound electron derives the levels underlying the formula.

• Band structureNarrower topic: Solving it with a periodic crystal potential yields the allowed energy states.

• Azimuthal quantum numberNarrower topic: Solving it for hydrogen-like atoms yields the orbital quantum numbers, including ℓ.

• First-principles calculationNarrower topic: First-principles methods derive material predictions from its many-particle form.

• Ehrenfest theoremNarrower topic: Ehrenfest's theorem follows by differentiating expectation values using this state evolution.

• Free particleNarrower topic: The free-particle case is the Schrödinger equation with only kinetic energy in its Hamiltonian.

• Walter KohnNarrower topic: Density functional theory offers a way to handle electronic systems without solving the full many-electron equation directly.

• Pauli equationNarrower topic: The Pauli equation extends this framework to include spin and magnetic coupling.

• Douglas HartreeNarrower topic: Hartree sought approximate solutions for multi-electron atoms where direct solutions were impractical.

• Hellmann–Feynman theoremNarrower topic: Differentiating its eigenvalue form yields the theorem’s central identity.

• Hyperspherical methodNarrower topic: The method reorganizes this equation for few-particle relative motion.

• Quantum speed limit theoremsNarrower topic: Its dynamics are the starting point for standard time-independent speed limits.