Key Concepts: Quantum Mechanics

Key Principles

• Wave-Particle Duality: All matter exhibits both wave and particle properties. λ = h/p.
• Quantization: Energy, angular momentum, and other properties come in discrete amounts.

The Wavefunction (ψ)

• The wavefunction describes the quantum state of a particle.
• |ψ|² gives the probability density of finding the particle at a given position.
• The wavefunction evolves according to the Schrödinger equation.

Heisenberg's Uncertainty Principle

• It is impossible to simultaneously know both the exact position and momentum of a particle:
• Δx · Δp ≥ ℏ/2 (where ℏ = h/2π).
• This is not a measurement limitation — it's a fundamental property of nature.

Quantum Tunneling: A particle can pass through a potential barrier even if its energy is less than the barrier height — there is a nonzero probability of being found on the other side.