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 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.

PATH INTEGRAL APPROACH TO A SINGLE POLYMER CHAIN WITH RANDOM MEDIA

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1465-1478 ◽  
Author(s):  
CH. KUNSOMBAT ◽  
V. SA-YAKANIT
Keyword(s):  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Short Range Correlation ◽  
Range Correlation ◽  
End Distance ◽  
Non Local ◽  
The Mean

In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.

A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS

2004 ◽  
Vol 07 (04) ◽  
pp. 507-526 ◽  
Author(s):  
S. ALBEVERIO ◽  
G. GUATTERI ◽  
S. MAZZUCCHI
Keyword(s):  
Phase Space ◽  
Continuous Measurement ◽  
Quantum Particle ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Infinite Dimensional ◽  
Feynman Path Integrals ◽  
Characteristics Method ◽  
Stochastic Characteristics

The Belavkin equation, describing the continuous measurement of the momentum of a quantum particle, is studied. The existence and uniqueness of its solution is proved via analytic tools. A stochastic characteristics method is applied. A rigorous representation of the solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the phase space is also given.

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