What is variational principle?

The variational principle is a fundamental principle in physics and mathematics that states that the actual behavior of a system will be such that a certain integral (called the action) will be minimized or maximized. This principle is often used to derive the equations of motion for a given system.

One of the most well-known applications of the variational principle is in the field of classical mechanics, where it is used to derive the principle of least action, which states that the action of a physical system will be minimized along the path that the system takes through time.

The variational principle also has applications in quantum mechanics, where it is used to derive the Schrödinger equation, which describes the wave function of a quantum system.

In mathematics, the variational principle is used in the calculus of variations, which is a field of mathematics concerned with finding functions that minimize or maximize certain functionals.

Overall, the variational principle is a powerful and versatile tool that has applications in a wide range of fields, including physics, mathematics, and engineering.