List of quantum-mechanical systems with analytical solutions

In quantum mechanics, certain systems can be solved exactly, yielding analytical solutions for their wave functions and energies. Here is a list of notable quantum-mechanical systems that have analytical solutions: 1. **Free Particle**: The simplest system, where a particle is not subjected to any forces. The solutions are plane waves. 2. **Infinite Square Well (Particle in a Box)**: A particle confined in a box with infinitely high walls.