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 (aka "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

Miscellaneous

• Quantum potential
• Pseudopotential
• Superpotential
• Kolos–Wolniewicz potential