This is a list of potential energy functions that are frequently used in quantum mechanics and have any meaning.
One-dimensional potentials Rectangular potential barrier Delta potential (a.k.a. "contact potential") Double delta potential Step potential Periodic potential Barrier potential Gaussian potential Eckart potential
Wells Quantum well Potential well Finite potential well Infinite potential well Double-well potential Semicircular potential well Circular potential well Spherical potential well Triangular potential well
Interatomic potentials Interatomic potential Bond order potential EAM potential Coulomb potential Buckingham potential Lennard-Jones potential Morse potential Morse/Long-range potential Rosen–Morse potential Trigonometric Rosen–Morse potential Stockmayer potential Pöschl–Teller potential Axilrod–Teller potential Mie potential
Oscillators Harmonic potential (harmonic oscillator) Morse potential (morse oscillator) Morse/Long-range potential (Morse/Long-range oscillator) Kratzer potential (Kratzer oscillator)
Quantum Field theory Yukawa potential Coleman–Weinberg potential Uehling potential Woods–Saxon potential Cornell potential
Miscellaneous Quantum potential Pseudopotential Superpotential Komar superpotential Kolos–Wolniewicz potential
See also List of quantum-mechanical systems with analytical solutions List of integrable models