scholarly journals p-Adic Path Integrals for Quadratic Actions

1997 ◽  
Vol 12 (20) ◽  
pp. 1455-1463 ◽  
Author(s):  
G. S. Djordjević ◽  
B. Dragovich
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Probability Amplitude ◽  
Exact Form ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
One Dimensional ◽  
Ordinary Quantum

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude [Formula: see text] for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

NELSON'S STOCHASTIC MECHANICS BY MEANS OF FEYNMAN PATH INTEGRALS

2000 ◽  
Vol 14 (03) ◽  
pp. 73-78 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Order Equation ◽  
Feynman Path Integral ◽  
Stochastic Mechanics ◽  
Path Integral Formulation ◽  
Feynman Path ◽  
First Order ◽  
Feynman Path Integrals

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

STATIONARY PHASE, QUANTUM MECHANICS AND SEMI-CLASSICAL LIMIT

1996 ◽  
Vol 08 (08) ◽  
pp. 1161-1185 ◽  
Author(s):  
JORGE REZENDE
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Stationary Phase ◽  
Finite Number ◽  
Path Integral ◽  
Critical Points ◽  
Classical Limit ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path

A method of stationary phase for the normalized-oscillatory integral on Hilbert space is developed in the case where the phase function has a finite number of critical points which are non-degenerate. Applications to the Feynman path integral and the semi-classical limit of quantum mechanics are given.

scholarly journals On the Feynman path integral for the magnetic Schrödinger equation with a polynomially growing electromagnetic potential

2019 ◽  
Vol 32 (01) ◽  
pp. 2050003 ◽  
Author(s):  
Wataru Ichinose
Keyword(s):  
Path Integral ◽  
Path Integrals ◽  
Continuous Functions ◽  
Time Variable ◽  
Electromagnetic Potential ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Spatial Direction ◽  
Electromagnetic Potentials ◽  
Feynman Path Integrals

The Feynman path integrals for the magnetic Schrödinger equations are defined mathematically, in particular, with polynomially growing potentials in the spatial direction. For example, we can handle electromagnetic potentials [Formula: see text] such that [Formula: see text] “a polynomial of degree [Formula: see text] in [Formula: see text]” [Formula: see text] and [Formula: see text] are polynomials of degree [Formula: see text] in [Formula: see text]. The Feynman path integrals are defined as [Formula: see text]-valued continuous functions with respect to the time variable.

scholarly journals Feynman Path Integral in Multiple-Slit and its Simulation

2019 ◽  
Vol 2 (1) ◽  
pp. 63-70
Author(s):  
Mahendra Satria Hadiningrat
Keyword(s):  
Interference Pattern ◽  
Path Integral ◽  
Electron Distribution ◽  
Analytic Solution ◽  
Integral Formula ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
One Dimensional ◽  
The One ◽  
Theoretical Results

In this article we hold on an analytic solution of the well-known cases of difraction and interference of electrons through one and two slits (simply that, the one-dimensional case is assumed only). In addition, we hold an approximations of the electron distribution which offer the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could also serve an awesome introduction to multiple slits interference. Then it is comparing between theoretical results and simulation in order to get interference pattern of it.

scholarly journals Adelic Path Integrals for Quadratic Lagrangians

2003 ◽  
Vol 06 (02) ◽  
pp. 179-195 ◽  
Author(s):  
Goran S. Djordjević ◽  
Branko Dragovich ◽  
Ljubiša Nešić
Keyword(s):  
Quantum Mechanics ◽  
General Formula ◽  
Path Integral ◽  
Path Integrals ◽  
Number Fields ◽  
One Dimensional ◽  
Adelic Quantum Mechanics

Feynman's path integral in adelic quantum mechanics is considered. The propagator [Formula: see text] for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is invariant under interchange of the number fields ℝ and ℚp.

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