Schrödinger Equation

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📖Definition

Schrödinger equation describes time evolution of wave function in quantum mechanics. Predicts quantum states.

i\hbar (∂ Ψ)/(∂ t) = \hatHΨ

Time-dependent Schrödinger equation

\hatHψ = Eψ

Time-independent Schrödinger equation

\hatH = -(\hbar²)/(2m)∇² + V

Hamiltonian operator

|Ψ(x,t)|² = probability density

Wave function interpretation

예제 1

Energy levels in infinite well (length L)?

Discovered by: Erwin Schrödinger (1926)

Mathematically formulated de Broglie's matter wave concept; 1933 Nobel Prize

Molecular structure, bonds

Electron band structure

Quantum dots, tunneling

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