Equations · Physics
Schrödinger equation
How the quantum state of a system changes in time.
iħ ∂ψ/∂t = Ĥψ
Aethel says
i h bar the partial derivative of psi with respect to t equals H hat psi
What it says
The wave function ψ holds everything that can be known about a quantum system. The equation says its rate of change is set by the Hamiltonian, the operator for the total energy.
Its solutions give the energy levels of atoms and the shapes of their orbitals.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| i | i | the imaginary unit |
| ħ | h bar | the reduced Planck constant, about 1.055 × 10⁻³⁴ J·s |
| ψ | psi | the wave function |
| Ĥ | H hat | the Hamiltonian operator; a hat marks an operator |
More on∂Partial derivativeψPsiħh-bar (reduced Planck constant)x̂Hat
Where you meet it
Quantum mechanics and quantum chemistry.
Questions
How do you say Schrödinger equation out loud?
iħ ∂ψ/∂t = Ĥψ is read: “i h bar the partial derivative of psi with respect to t equals H hat psi.” That is exactly what Aethel says when it meets the formula in a book.
What does i mean in Schrödinger equation?
i (said “i”) is the imaginary unit.
What does ħ mean in Schrödinger equation?
ħ (said “h bar”) is the reduced Planck constant, about 1.055 × 10⁻³⁴ J·s.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.