scholarly journals Nonstandard Feynman path integral for the harmonic oscillator

1999 ◽  
Vol 40 (11) ◽  
pp. 5511-5521 ◽  
Author(s):  
Ken Loo
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Feynman Path Integral ◽  
Feynman Path

JOINT ENTROPY OF THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT MASS AND/OR FREQUENCY

2009 ◽  
Vol 23 (11) ◽  
pp. 2449-2461 ◽  
Author(s):  
ETHEM AKTÜRK ◽  
ÖZGÜR ÖZCAN ◽  
RAMAZAN SEVER
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Method ◽  
Time Dependent ◽  
Joint Entropy ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Path Integral Method ◽  
Dependent Mass

Time-dependent joint entropy is obtained for harmonic oscillator with the time-dependent mass and frequency case. It is calculated by using time-dependent wave function obtained via Feynman path integral method. Variation of time dependence is investigated for various cases.

FEYNMAN PATH INTEGRAL REPRESENTATIONS FOR THE CLASSICAL DAMPED HARMONIC OSCILLATOR WITH STOCHASTIC FREQUENCY

2002 ◽  
Vol 16 (21) ◽  
pp. 793-806 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Integral Solution ◽  
Integral Representations ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Damped Harmonic Oscillator

We propose a Feynman path-integral solution for classical damped harmonic oscillator motions with stochastic frequency.

scholarly journals Ultra-light and strong: The massless harmonic oscillator and its singular path integral

2016 ◽  
Vol 14 (01) ◽  
pp. 1750010
Author(s):  
Giovanni Modanese
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
High Frequency ◽  
Classical Mechanics ◽  
Planck Equation ◽  
Initial Position ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Limit Formula ◽  
Hilbert Action

In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes completely de-localized in the limit [Formula: see text]. The harmonic oscillator thus ceases to be a useful microscopic physical model in the limit [Formula: see text], but its Feynman path integral has interesting singularities which make it a prototype of other systems exhibiting a “quantum runaway” from the classical configurations near the minimum of the action. The probability density of the coherent runaway modes can be obtained as the solution of a Fokker–Planck equation associated to the condition [Formula: see text]. This technique can be applied also to other systems, notably to a dimensional reduction of the Einstein–Hilbert action.

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.

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