The rulebook for the blur
If a quantum particle is a spreading, sloshing wave of possibility, something has to say how it sloshes over time. The Schrödinger equation is that rulebook — the equation that predicts how the wavefunction evolves from one moment to the next.
How a quantum state evolves
The time-dependent Schrödinger equation, iℏ ∂ψ/∂t = Ĥψ, governs how a wavefunction changes in time. Ĥ is the Hamiltonian operator — it encodes the system's total energy (kinetic + potential).
Stationary states
Solving Ĥψ = Eψ gives energy eigenstates with definite energy E. Their probability density |ψ|² doesn't change in time — hence 'stationary'.
Lab · Read the equation
- Identify the operator acting on ψ on the right side.
- Note what E represents in Ĥψ = Eψ.
- Recall what stays constant for an eigenstate.
What you should see: Ĥ is the energy operator; E is the state's definite energy; |ψ|² is constant in time for an eigenstate.