Quantum Mechanics — Core Equations
1. Wave function and probability
The wave function describes a quantum state; its squared magnitude determines position
probabilities.
2. Schrodinger equation
The Hamiltonian generates the time evolution of a closed nonrelativistic quantum system.
3. Operators and uncertainty
Noncommuting observables obey an uncertainty relation.
4. State expansion and Born rule
Measurement probabilities follow from projection amplitudes.
5. Expectation value and variance
Expectation values describe ensemble averages.
6. Infinite square well
Boundary conditions produce discrete stationary energies.
7. Harmonic oscillator
Creation and annihilation operators reveal the oscillator spectrum.
8. Angular momentum and spin
Angular momentum is quantized and its Cartesian components do not commute.
9. Time evolution
For a time-independent Hamiltonian, evolution is unitary.
10. Two-level quantum system
A normalized pure qubit state can be parameterized by two angles.