LaTeX
i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat H|\psi(t)\rangleVariables
- ħ: reduced Planck constant
- |ψ(t)⟩: state vector
- Ĥ: Hamiltonian operator
How to use this formula
Describes the time evolution of a quantum state under a Hamiltonian.
Important notes
- The Hamiltonian and boundary conditions define the physical system.
Quick example
For a time-independent energy eigenstate, evolution adds a phase factor.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The Hamiltonian and boundary conditions define the physical system.
- For the Time-Dependent Schrödinger Equation, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- State the Hilbert-space, normalization, operator, basis, and unit conventions used in the calculation.
Worked example
For a time-independent energy eigenstate, evolution adds a phase factor.
Common mistakes
- When copying Time-Dependent Schrödinger Equation, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Time-Dependent Schrödinger Equation with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Time-Dependent Schrödinger Equation in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat H|\psi(t)\rangle. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Time-Dependent Schrödinger Equation used for?
Describes the time evolution of a quantum state under a Hamiltonian.
Can I copy this formula as LaTeX?
Yes. Copy i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat H|\psi(t)\rangle or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.