Related papers: Partition Function of the Harmonic Oscillator on a…
For the model of a linearly driven quantum anharmonic oscillator, the role of damping is investigated. We compare the position of the stable points in phase space obtained from a classical analysis to the result of a quantum mechanical…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for…
We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
We study some complete orthonormal systems on the real-line. These systems are determined by Bargmann-type transforms, which are Fourier integral operators with complex-valued quadratic phase functions. Each system consists of…
Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the…
We show the existence of a continuum of Hamiltonian structures for the two-dimensional isotropic harmonic oscillator. In particular, a continuum of Hamiltonian structures having noncommutative coordinates is presented. A study of the…
Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave…
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of…
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
We analyze the symmetries in an open quantum system composed by three coupled and detuned harmonic oscillators in the presence of a common heat bath. It is shown analytically how to engineer the couplings and frequencies of the system so as…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
In this paper, we present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same…
The two-dimensional relativistic configurational $\vec r$-space is proposed and the exactly solvable finite-difference model of the harmonic oscillator in this space is constructed. The wave functions of the stationary states and the…
I consider two identical quantum particles in two boxes. We can split each box, and thereby the wavefunction of each particle, into two parts. When two half boxes are interchanged and combined with the other halves, where do the two…