aqora

Quantization of a General Dynamical System by Feynman's Path Integration Formulation

K. S. Cheng

The Schrödinger equation is obtained by Feynman's path integration method of quantization for a general dynamical system. The meaning of the results is discussed.

Journal of Mathematical PhysicsNov 1, 1972152 citations

From Path Integration to the Schrödinger Equation

Lukong Cornelius Fai

We show how from the path integral we rederive the Schrödinger equation. This will confirm the Feynman path integration to be the formulation of quantum mechanics presenting an alternative way of examining the subject matter than the usual approaches with applications as vast as those of quantum mechanics itself.

CRC Press eBooksFeb 19, 20210 citations

Technique of Path Integrals

Michael B. Mensky

In the late forties Richard Feynman (1948) proposed a path-integral form of quantum mechanics that proved to be equivalent to the conventional Schrödinger-equation form but possessed a much more heuristic force (see Feynman and Hibbs (1965) for a detailed exposition of Feynman’s theory). Our consideration of continuous measurements in the following chapters will be based on Feynman path integrals. A theory of quantum continuous measurements will be formulated directly in terms of path integrals instead of a limiting process of the type used in Chapter 2 .In the late forties Richard Feynman (1948) proposed a path-integral form of quantum mechanics that proved to be equivalent to the conventional Schrödinger-equation form but possessed a much more heuristic force (see Feynman and Hibbs (1965) for a detailed exposition of Feynman’s theory). Our consideration of continuous measurements in the following chapters will be based on Feynman path integrals. A theory of quantum continuous measurements will be formulated directly in terms of path integrals instead of a limiting process of the type used in Chapter 2 .

CRC Press eBooksOct 19, 20170 citations

On convergence of the Feynman path integral in phase space

Wataru Ichinose

It was an interested and important problem to give the description of quantization, i.e. of passing from classical physical systems to the corresponding quantum ones, from the moment that quantum mechanics came into existence. In the end we succeeded in giving it as follows: Let L be a Lagrangian function. Then the Hamiltonian function H is defined through the Legendre transformation of L. The Hamiltonian operator ( ) at time in quantum mechanics is defined from H. It should be noted that ( ) has ordering ambiguities (cf. [14]). Let be a probability amplitude at time . Then its temporal evolution can be given by the solution of the Schrodinger equationIt was an interested and important problem to give the description of quantization, i.e. of passing from classical physical systems to the corresponding quantum ones, from the moment that quantum mechanics came into existence. In the end we succeeded in giving it as follows: Let L be a Lagrangian function. Then the Hamiltonian function H is defined through the Legendre transformation of L. The Hamiltonian operator ( ) at time in quantum mechanics is defined from H. It should be noted that ( ) has ordering ambiguities (cf. [14]). Let be a probability amplitude at time . Then its temporal evolution can be given by the solution of the Schrodinger equation

Osaka Journal of MathematicsMar 1, 20021 citation

Feynman path integrals and the Schrödinger equation

WORLD SCIENTIFIC eBooksDec 1, 20210 citations

Feynman Path Integrals and the Schrödinger Equation

WORLD SCIENTIFIC eBooksMay 1, 20092 citations

On normalization problems of the path integral method

Abstract

Related papers

On normalization problems of the path integral method

Abstract

Related papers