quantum physics

Quantum Mechanics

Fundamental Equations

• Schrödinger Equation: $$ i\hbar \frac{\partial \psi}{\partial t} = \hat{H} \psi $$
• Heisenberg Uncertainty Principle: $$ \Delta x \Delta p \geq \frac{\hbar}{2} $$

Quantum States and Operators

• Wavefunction: $$ \Psi(x, t) $$
• Expectation Value: $$ \langle A \rangle = \int \Psi^* \hat{A} \Psi dx $$
• Operator: $$ \hat{A} $$

Quantum Mechanics in Different Representations

• Position Representation: $$ \langle x | \psi \rangle = \psi(x) $$
• Momentum Representation: $$ \langle p | \psi \rangle = \phi(p) $$

Quantum Mechanics and Electromagnetism

• Quantum Electrodynamics (QED): Describes the interaction between light and matter.
• Quantum Chromodynamics (QCD): Describes the strong force between quarks.