Related papers: Extended Feynman Formula for the Harmonic Oscillat…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
By returning to the underlying discrete time formalism, we relate spurious results in coherent state path integral calculations to the high frequency structure of their propagators. We show how to modify the standard expressions for…
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
The harmonic oscillator Hamiltonian, when augmented by a non-Hermitian $\cal{PT}$-symmetric part, can be transformed into a Hermitian Hamiltonian. This is achieved by introducing a metric which, in general, renders other observables such as…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
This paper reviews and generalizes Feynman's path integration methods which use time slicing with straight line segments and Fourier sine series. The generalizations are done from variational calculus considerations and in one dimension for…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…
An efficient continuous-time path-integral Quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting…
We derive the partition function of the one-body and two-body systems of classical noncommutative harmonic oscillator in two dimensions. Then, we employ the path integral approach to the quantum noncommutative harmonic oscillator and derive…
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical…