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The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
Path integral molecular dynamics (PIMD) is a method of incorporating quantum mechanics into molecular dynamics simulations using Feynman path integrals. In PIMD, one uses the Born–Oppenheimer approximation to separate the wavefunction into a nuclear part and an electronic part. The nuclei are treated quantum mechanically by mapping each ...
Historically, as a book-keeping device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, [6] because the path integral was unfamiliar when they were introduced, and Freeman Dyson's derivation from old-fashioned perturbation theory borrowed from the perturbative expansions in statistical mechanics ...
In 1981, Schulman published Techniques and Applications of Path Integration, [4] from which many physicists learned about Feynman's path integral and its many applications. The book went on to become a Wiley classic and in 2005 came out in a Dover edition (with a supplement).
Feynman's algorithm is an algorithm that is used to simulate the operations of a quantum computer on a classical computer. It is based on the Path integral formulation of quantum mechanics , which was formulated by Richard Feynman .
Functional integrals where the space of integration consists of paths (ν = 1) can be defined in many different ways. The definitions fall in two different classes: the constructions derived from Wiener's theory yield an integral based on a measure, whereas the constructions following Feynman's path integral do not. Even within these two broad ...
According to the Feynman path-integral formulation of quantum mechanics, the path of the quantum object is described mathematically as a weighted average of all those possible paths. In 1966 an explicitly gauge invariant functional-integral algorithm was found by DeWitt , which extended Feynman's new rules to all orders.
Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral (2nd ed.). World Scientific. ISBN 9789814397735. Sakurai, J. J.; Napolitano, Jim (2017). Modern Quantum Mechanics (2nd ed.). Cambridge University Press. ISBN 978-1-108-42241-3. Leonard I. Schiff (1968) Quantum Mechanics McGraw-Hill Education