Schrödinger Equation
Definition
The master equation of quantum mechanics — it dictates how the quantum wave describing a particle evolves in time.
Technical definition
iℏ∂ψ/∂t = Ĥψ. The time-independent form Ĥψ = Eψ yields quantized energy levels; |ψ|² is the probability density (Born rule).
Example
Solving it for hydrogen predicts the exact spectral lines — the red 656 nm H-alpha line falls straight out of the mathematics.
Common confusion
The wavefunction ψ is not a physical wave sloshing around — it is a probability amplitude. Only |ψ|² connects to measurable reality.