nLab Morse potential

Morse potential is one of the standard 1-dimensional potentials which are used mainly in quantum mechanics (especially in atomic and molecular physics). If $r$ is the coordinate (say, the distance between atoms) in $\mathbb{R}_+$, and $l, D$ constants ($l$ being the scale of the system) then one of the standard forms of Morse potential is

$$V(r) = D (e^{- 2 x/l} - 2 e^{-x/l})$$

up to addition of physically irrelevant constant summand this is the same as $D (1 - exp(-x/l))^2$.

• wikipedia Morse potential
• P. M. Morse, Diatomic molecules according to the wave mechanics. II. Vibrational levels, Phys. Rev. 34, 57-64 (1929)
• B Molnár, M G Benedict, J Bertrand, Coherent states and the role of the affine group in the quantum mechanics of the Morse potential, J. Phys. A34, n.14, 3139-3151 (2001) doi
• Jens Peder Dahl, Michael Springborg, The Morse oscillator in position space, momentum space, and phase space, J. Chem. Physics 88, 4535 (1988) doi
• C. Quesne, Revisiting (quasi-)exactly solvable rational extensions of the Morse potential, Internat. J. Modern Phys. A 27 (2012) no. 13, 1250073, 18 pp. MR2926659 doi

category: physics