Lecture Notes

Introduction to Quantum Mechanics

Key Concepts

• Quantum mechanics is a fundamental theory in physics.
• Describes physical properties of nature at the scale of atoms and subatomic particles.

Historical Context

• Emerged in the early 20th century.
• Key figures: Max Planck, Albert Einstein, Niels Bohr.
• Planck's quantum theory (1900): energy is quantized.
• Einstein's photoelectric effect (1905): light has particle-like properties.
• Bohr's model of the atom (1913): electrons exist in quantized shells.

Fundamental Principles

• Wave-particle duality: particles exhibit both wave and particle properties.
• Heisenberg uncertainty principle: precise measurement of certain pairs of properties (e.g., position and momentum) is impossible.
• Schrödinger equation: describes how the quantum state of a physical system changes over time.

Quantum States

• Represented by wave functions.
• Probability distributions: describe the likelihood of finding a particle in a particular state.
• Superposition: a quantum system can be in multiple states simultaneously.
• Entanglement: particles become interconnected and the state of one can instantaneously affect the state of another, regardless of distance.

Applications

• Quantum computing: exploits superposition and entanglement to perform computations more efficiently than classical computers.
• Quantum cryptography: uses principles of quantum mechanics to create secure communication channels.
• Quantum teleportation: transfer of quantum states from one particle to another.