quantum

## What I do - Apply wave-particle duality concepts - Analyze quantum state evolution - Model quantum entanglement and Bell inequalities - Calculate transition probabilities - Study quantum measurement and wave function collapse - Apply selection rules for allowed transitions ## When to use me When studying quantum information, quantum computing, or fundamental quantum physics. ## Key Concepts - **de Broglie Wavelength**: λ = h/p relates momentum to wave nature - **Born Rule**: Measurement yields eigenvalues with probabilities |⟨a|ψ⟩|² - **Entanglement**: Non-classical correlations between quantum particles - **Heisenberg Picture**: Operators evolve, states fixed; vs Schrödinger picture - **Commutators**: [A, B] = AB - BA, [x, p] = iℏ - **Density Matrix**: ρ = |ψ⟩⟨ψ| for pure states, Tr(ρ²) < 1 for mixed