Quantum Mechanics

Quantum Mechanics Overview

Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales. It provides a mathematical framework for understanding the wave-particle duality of particles and the probabilistic nature of quantum systems.

Key Concepts in Quantum Mechanics

1. Superposition

Superposition is a fundamental principle in quantum mechanics that states that a physical system exists in all possible states simultaneously until it is measured.

Equation:

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩$$

• $|\psi ⟩$ represents the quantum state of a system
• The coefficients $\alpha$ and $\beta$ are complex numbers
• $|0⟩$ and $|1⟩$ are the basis states.

2. Entanglement

Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the quantum state of one particle cannot be described independently of the others.

Equation:

$$|\psi ⟩=\frac{1}{\sqrt{2}}\left(|00⟩+|11⟩\right)$$

• $|00⟩$ and $|11⟩$ are the Bell states
• The particles are said to be entangled if they share a Bell state.