Quantum Mechanics Basics
Wave Function
State of a quantum system:
$$ |\psi\rangle = \sum_i c_i |i\rangle $$
Normalization: $\langle\psi|\psi\rangle = 1$
Born Rule
Probability of measuring state $|i\rangle$:
$$ P(i) = |\langle i|\psi\rangle|^2 = |c_i|^2 $$
Expectation Value
$$ \langle A \rangle = \langle\psi|\hat{A}|\psi\rangle $$
Uncertainty Principle
$$ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} $$
Further Reading
Related Snippets
- Path Integral Formulation
Feynman's path integral approach to quantum mechanics - Quantum Computing Basics
Qubits, gates, and quantum algorithms - Quantum Operators
Position, momentum, and Hamiltonian operators - Schrödinger Equation
Time-dependent and time-independent formulations