- #1
wenty
- 20
- 0
Does anyone know where to find the "direct" (not by prove they are both equal to Schrodinger formualtion )proof?
The path integral formulation and the matrix formulation are two different mathematical approaches used to describe the behavior of quantum systems. The path integral formulation is based on the concept of a particle taking all possible paths simultaneously, while the matrix formulation uses matrices to represent the operators and states of a quantum system.
The path integral formulation and the matrix formulation are equivalent, meaning they can both be used to describe the same quantum system. The path integral can be converted into a matrix expression through a process called discretization, where the continuous path is divided into a finite number of steps.
The path integral formulation allows for a more intuitive understanding of quantum mechanics, as it is based on the concept of a particle taking all possible paths. It also provides a way to deal with non-perturbative effects, which are difficult to handle in the matrix formulation.
The matrix formulation is more mathematically rigorous and can handle a wider range of quantum systems, including those with an infinite number of states. It is also more computationally efficient, making it easier to apply to complex systems.
Both the path integral and matrix formulation are used extensively in research, as they each have their own advantages and are applicable to different types of systems. However, the matrix formulation is more commonly used in theoretical physics, while the path integral formulation is often used in condensed matter physics and quantum field theory.