Related papers: Extended Feynman Formula for the Harmonic Oscillat…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of…
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schr\"odinger equation yields real eigenvalues with complex eigenfunctions. We…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well-defined. In particular, it is consistent…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…
We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…