相关论文: The Degenerate Parametric Oscillator and Ince's Eq…

For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…

In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…

We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the $SU(1,1)$ and $SU(2)$ groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its…

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

A size-extensive, converging, black-box, ab initio coupled-cluster ($\Delta$CC) ansatz is introduced that computes the energies and wave functions of stationary states from any degenerate or nondegenerate Slater-determinant references with…

The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.

Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…

We construct the Perelomov number coherent states for any three $su(1,1)$ Lie algebra generators and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the $su(1,1)$ Lie…

A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…

By using the complete solution of the Milburn equation (beyond the Lindblad form that it is generally used) that describes intrinsic decoherence, we study the decaying dynamics of a displaced harmonic oscillator. We calculate the…

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson…

The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…

In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…

We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…

Using gauge invariant quark Green's functions, defined with path-ordered gluon field phase factors along polygonal lines, and functional relations among them, two compatible bound state equations of the Dirac type are established for…

We consider canonically conjugated generalized space and linear momentum operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a generalized translation operator which produces infinitesimal deformed displacements…

The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…

We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…

Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…

The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive…