The Schrödinger equation is a partial differential equation that describes the behavior of quantum mechanical systems, such as atoms and molecules. It provides a mathematical framework for understanding the behavior of these systems and predicts their evolution over time. The equation takes the form:
iℏ ∂Ψ/∂t = HΨ
where i is the imaginary unit, ℏ (h-bar) is a constant that relates the energy and frequency of a quantum system, Ψ is the wave function of the system, t is time, and H is the Hamiltonian operator, which describes the total energy of the system.
For example, consider the simple case of a particle in a one-dimensional potential well. The potential well is defined as a region where the particle is confined, such as a box with walls that the particle cannot penetrate. The Schrödinger equation can be used to find the wave function of the particle in the potential well, which gives information about its behavior and possible energy states. |
