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

• Quantum theoryRelated: It specifies continuous state evolution between measurements in nonrelativistic quantum mechanics.

• Sommerfeld modelCompared with: Its wave solutions superseded Sommerfeld’s prescribed classical-like electron orbits.

• WKB approximationRelated: The one-dimensional stationary equation is the standard setting for quantum WKB.

• Hamiltonian operatorRelated: The Hamiltonian determines the generator of time evolution in its time-dependent form.

• Hydrogen-like atomRelated: Solving it for a Coulomb potential yields the hydrogen-like atom’s wavefunctions and energy levels.

• Nearly-free-electron modelRelated: Solving it with a periodic potential yields the model's electron states.

• Wave mechanicsRelated: It supplies the central dynamical law for wavefunctions.

• Wigner’s friendRelated: Wigner can apply this unitary evolution to the entire laboratory, including the friend.

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

• Bohr radiusRelated: Its hydrogen ground-state wavefunction has a radial scale equal to the Bohr radius.

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

• Linear combination of atomic orbitalsRelated: Molecular orbitals constructed by LCAO are approximate solutions to this equation.

• Particle in a boxRelated: Its stationary form determines the particle’s allowed wavefunctions and energies.

• Spherical coordinate systemRelated: Spherical coordinates separate variables for quantum systems with central potentials.

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

• Momentum operatorRelated: Momentum enters its Hamiltonian through kinetic energy and through coupling to fields.

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

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

• Hugh Everett IIIRelated: Its uninterrupted evolution is central to Everett’s account of measurement.

• Atomic unitsRelated: Atomic units remove several constants from its nonrelativistic form for atomic systems.

• 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.

• Theoretical chemistryRelated: Its molecular solutions underpin predictions of electronic structure and chemical properties.

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

• Wave packetRelated: Its solutions show how a quantum wave packet spreads or propagates.

• De Broglie–Bohm theoryRelated: Bohmian theory retains its standard evolution for the guiding wave.

• Modern physicsBroader topic: It gives quantum mechanics a precise rule for time evolution.

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

• Quantum potentialRelated: Rewriting it in amplitude-and-phase form yields the quantum potential term.

• Time derivativeRelated: Its time-dependent form relates the state vector's time derivative to energy.

• Crank–Nicolson methodRelated: Crank–Nicolson is used for its time evolution because the discretization can preserve norm.

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

• Finite potential wellRelated: Its solutions inside and outside the well determine the bound-state energies and leakage.

• Atomic and molecular structureRelated: Its solutions provide the wavefunctions used to calculate electron structure.

• Atomic propertiesRelated: Its solutions yield the allowed electron states and energies of atoms.

• Atomic systemRelated: It predicts how atomic wave functions evolve under a specified Hamiltonian.

• Bra–ket notationRelated: Its state vector can be written as a time-dependent ket.

• De Broglie equationRelated: It develops wave descriptions of matter beyond the wavelength-momentum relation.

• Delta potentialRelated: Solving it across the point interaction determines the wavefunction and its derivative jump.

• Evolution (physics)Broader topic: It is the standard law of quantum-state evolution in nonrelativistic quantum mechanics.

• Foundations of quantum mechanicsRelated: Its continuous evolution contrasts with the discontinuous state update associated with measurement.

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

• History of subatomic physicsRelated: Its use turned quantum theory into a tool for predicting atomic behavior.

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

• Mathematical formulation of quantum mechanicsRelated: It gives the standard continuous-time law for closed-system state evolution.

• Position and momentum spacesRelated: Its form can be simpler in one representation depending on the system's Hamiltonian.

• Potential wellRelated: Its solutions give the allowed energies and wavefunctions inside a quantum well.

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

• Quantum tunnellingRelated: Its solutions determine how a particle’s wavefunction extends into and beyond a barrier.

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