quantum-mechanics

## What I do - Solve Schrödinger equation for various potentials - Analyze quantum mechanical operators and observables - Model quantum tunneling and barrier penetration - Calculate expectation values and probability distributions - Study angular momentum and spin systems - Apply perturbation theory for approximate solutions ## When to use me When analyzing atomic, molecular, or subatomic systems, or designing quantum devices. ## Key Concepts - **Schrödinger Equation**: iℏ∂ψ/∂t = Ĥψ, time-independent: Ĥψ = Eψ - **Wave Function**: |ψ|² gives probability density, normalized ∫|ψ|²dτ = 1 - **Uncertainty Principle**: ΔxΔp ≥ ℏ/2, ΔEΔt ≥ ℏ/2 - **Quantum Harmonic Oscillator**: E_n = (n + ½)ℏω, quantized energy levels - **Tunneling**: Probability T ≈ e^{-2γd} through potential barriers - **Spin**: s = ½ for electrons, Pauli exclusion principle for fermions