What is path integral?

In this section, you will make your first acquaintance with path integral. In quantum theory, path integral is a method of constructing the propagator. So we begin with the propagator.

What is the path integral of Lagrangian?

where S [ x] is the action of the system, and ∫ D x is the so-called path integral. Next, we carefully examine the above equation. Take 1D free particle for example. The Lagrangian of 1D free particle is Suppose we now work on the start point x, t and end point x ′, t ′. The path integral requires “integrating along all paths”.

What is the propagator in quantum mechanics?

As a consequence, K ( x, t; x ′, t ′) is called the propagator. The previous argument is only one way to construct Quantum Mechanics, i.e. suppose the Schrödinger equation holds -> derivation of the propagator.