Time-Dependent Schrödinger Equation

i\hbar\frac{\partial \Psi}{\partial t} = \hat{H}\Psi

The fundamental equation of quantum mechanics describing how quantum states evolve in time.

Variables

Imaginary unit

unitless

ℏ

Reduced Planck constant

J·s

Wave function

unitless

Ĥ

Hamiltonian operator

unitless

Your notes

0/5000

Constants in this formula

ℏ

Reduced Planck Constant

1.054 571 817… × 10⁻³⁴. Exact by definition.

J·s

Other modern physics formulas with the same quantities

Energy-Time Uncertainty (Quantum Mechanics) shares Reduced Planck constant
Fermi Energy (Quantum Mechanics) shares Reduced Planck constant
Bohr Radius (Atomic Physics) shares Reduced Planck constant

Where this formula is listed

Modern Physics formulas, under Quantum Mechanics, alongside Photon Energy (Planck), Photoelectric Effect, Stopping Potential, de Broglie Wavelength and Particle in a Box Energy Levels.
In the modern physics list it comes after Energy-Time Uncertainty and before Particle in a Box Energy Levels.
Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Time-Dependent Schrödinger Equation formula?

Time-Dependent Schrödinger Equation is written iℏ(∂Ψ/∂t) = ĤΨ. The fundamental equation of quantum mechanics describing how quantum states evolve in time. It belongs to Modern Physics, under Quantum Mechanics.

What are the units in iℏ(∂Ψ/∂t) = ĤΨ?

In SI units, i is imaginary unit (dimensionless); ℏ is reduced planck constant, measured in J·s; Ψ is wave function (dimensionless); Ĥ is hamiltonian operator (dimensionless).