Quantum Well — Bound State Calculator

Well Width L 2.00 nm

Well Depth V₀ 0.200 eV

Electric field perturbation
V′(x) = ε⋅(x + L/2)/L
(0 at left wall, ε at right wall)

Field strength ε 0.000 eV

Bound States & Energies

Displaying first 5 — all states used in perturbation sum

Finite square well solved numerically.
Even: z · tan(z) = √(z₀²−z²)
Odd: −z · cot(z) = √(z₀²−z²)

1st-order energy correction:
ΔEₙ = <n|V′|n> / <n|n>

1st-order wavefunction correction:
ψₙ¹ = ψₙ⁰ + Σₘ≠ₙ cₘₙ ψₘ⁰
cₘₙ = <m|V′|n> / (Eₙ−Eₘ)

Sum runs over all bound states found
(not capped at 5 displayed).

Well bottom = 0 eV • Top = +V₀

Potential & wavefunctions (ψ amplitude scaled for display)