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Physical Sciences
Quantum Mechanics
1926
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Schrödinger Equation

iℏ∂ψ∂t=H^ψi\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi

The wave function of a quantum system evolves according to its energy operator.

By Erwin Schrödinger

Physical Sciences
Schrödinger Equation
1926 · Erwin Schrödinger
Expert Reviewed
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Story PortalWho discovered this?Discover how Erwin Schrödinger and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — MRI scanners and semiconductors.Math PortalWhat does it derive from?Trace the mathematical lineage from de Broglie waves.Future PortalWhere is it going?Quantum computing and materials discovery
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Why it matters: Foundation of quantum chemistry, semiconductors, lasers, and modern technology.

Discoverers: Erwin Schrödinger (1926)

What does it mean?

The wave function of a quantum system evolves according to its energy operator.

Why should I care?

Foundation of quantum chemistry, semiconductors, lasers, and modern technology.

Equation Compass

North — Prerequisites

West — History

East — Applications

South — Derivations

Variables & Units

SymbolNameUnitMeaning
ψψWave function—Quantum state
H^\hat{H}Hamiltonian—Energy operator
ℏℏReduced Planck—h/(2π)

Worked Example

Particle in box: quantized energies E_n = n²h²/(8mL²).

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Pictures & video

Photograph of Erwin Schrödinger, 1933
Erwin Schrödinger, who formulated the wave equation of quantum mechanics (1926).Nobel Foundation / Wikimedia Commons · Public domain

Sources & further reading

Schrödinger equation — WikipediaSearch WikipediaSearch Wolfram MathWorldOpen in Wolfram|AlphaWatch explainers on YouTube

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Equation Universe

Schrödinger Equation

iℏ∂ψ∂t=H^ψi\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi

Real-world impact

Semiconductors & lasers

Quantum wavefunctions underpin transistors, LEDs, and quantum computing.

Photo: Unsplash — quantum computing

The wave function of a quantum system evolves according to its energy operator.

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