In quantum mechanics, the concept of potential energy is typically associated with particles rather than waves. Potential energy arises from the interactions between particles and their surroundings, such as the gravitational potential energy or the potential energy due to an electric field.
When it comes to quantum systems, including particles described by wave functions, potential energy can be incorporated into the mathematical description of the system. For example, in the Schrödinger equation, which is a fundamental equation in quantum mechanics, the potential energy is often included as a term in the equation to account for the influence of external forces or fields on the particle's behavior.
In the case of a quantum particle, the wave function describes the probability distribution of finding the particle in different states or locations. This distribution can change over time, and the behavior of the particle is determined by the dynamics of the wave function, which is influenced by various factors including the potential energy present in the system.
It's important to note that potential energy in quantum mechanics is not treated in the same way as in classical mechanics. In classical physics, potential energy is often associated with a specific location or position of a particle. In quantum mechanics, however, the wave function describes the probability distribution of the particle's position, and its energy is described by the wave function's associated eigenvalues.
Therefore, while the concept of potential energy can be incorporated into the mathematical framework of quantum mechanics, it is more closely associated with the particle-like aspects of quantum systems rather than the wave-like aspects.