2025/07/11 by Jianhao Li, Dominika Zgid, James K Freericks +1
Computer Science · Physics and Astronomy · #Mechanical and Optical Resonators #Neural Networks and Applications #Statistical Mechanics and Entropy
paper · doi:10.1088/1361-6404/adeee3
openalex publication_date 2025/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
Abstract The Morse potential is an important problem to examine due to its applications in describing vibrations and bond breaking in molecules. It also shares some properties with the simpler harmonic oscillator, at the same time displaying differences, allowing for an interesting contrast to its well-studied counterpart. The solution of the Morse potential is not usually taught in a quantum mechanics class, since using differential equations makes it very tedious. Here, we illustrate how to solve the Morse potential using the Schrödinger factorization method. This operator method is a powerful tool to find the energy eigenvalues, eigenstates, and wavefunctions without using differential equations in position space, allowing us to solve more problems without requiring a discussion of hypergeometric or confluent hypergeometric functions.