Schrödinger Operator & Bound States
Eigenvalue spectrum, bound states & spectral gaps in quantum wells
Potential
Type:
Square Well
Harmonic Oscillator
Double Well
Morse Potential
Periodic (Kronig-Penney)
Depth V₀:
5.00
Width a:
1.00
State n:
0
Energy Levels
Key Equations
Ĥψ = [-ℏ²/2m ∂²/∂x² + V(x)]ψ = Eψ
Square well: Eₙ = ℏ²π²n²/2mL²
SHO: Eₙ = ℏω(n+½)
Tunneling: T ~ e^{-2κd}, κ=√(2m(V-E))/ℏ