Quantum Morse Oscillator

Exact Energy Spectrum · Anharmonicity · Dissociation Limit

Well depth D (au) 8.0

Width α 1.0

Highlight level n 0

E_n = ℏω_e(n+½) − ℏω_e·χ_e·(n+½)²
where ℏω_e = α√(2D/μ) and χ_e = ℏω_e/(4D).
Maximum bound level: n_max = ⌊1/(2χ_e) − ½⌋. Levels converge at dissociation limit E=0. Wavefunctions ψ_n(x) are exact in terms of associated Laguerre polynomials.