Physics - Modern Physics - Quantum Mechanics - Perturbation theory - Perturbation Theory Problems

5 problems. P1: 'Particle in a box (width L) with perturbation H'=V₀ (constant) inside the entire box. First-order correction to Eₙ: Eₙ⁽¹⁾ = ⟨n|V₀|n⟩ = V₀∫|ψₙ|²dx = ___' (V₀ - all levels shift by same amount, trivial). P2: 'Now H' = V₀x/L (linear tilt). For n=1: E₁⁽¹⁾ = (2V₀/L²)∫₀ᴸ x sin²(πx/L)dx =