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Schrödinger equation (time-dependent)
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Governs the evolution of the wavefunction.
iħ∂ψ/∂t = Ĥψiħ ∂ψ/∂t = Ĥψ determines how the wavefunction evolves. It's linear, so superpositions evolve independently.
A free particle's ψ spreads over time.
Evolution is deterministic until measurement.
In more detail
The time-dependent Schrödinger equation iħ ∂ψ/∂t = Hψ governs how quantum states evolve over time. It is the fundamental dynamical equation of non-relativistic quantum mechanics.
Real-world uses
- Chemists use it to model molecular dynamics.
- Quantum computers implement its evolution in controlled systems.
- Physicists use the time-dependent Schrödinger equation to predict how a quantum system evolves in a laser pulse or a chemical reaction.
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Frequently asked questions
Is it like Newton's second law?
Yes in role, since it determines future states from the present, but it is a wave equation.
Why is there an i?
It makes the equation produce oscillating phases rather than exponential growth.
Is the Schrödinger equation a wave equation?
Yes, but the wave is the wavefunction, which is complex, and its evolution is deterministic even though measurements are probabilistic.
Related topics in Quantum Mechanics
Wavefunction · Born rule · Normalisation · Schrödinger equation (time-independent) · Operators and observables · Commutators