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