相关论文: Time-Dependent Diffeomorphisms as Quantum Canonica…
Time-dependent unitary transformations are used to study the Schreodinger equation for explicitly time-dependent Hamiltonians of the form $H(t)=\vec R(t).\vec J$, where $\vec R$ is an arbitrary real vector-valued function of time and $\vec…
We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is…
We investigate the relation between the invariant operators satisfying the quantum Liouville-von Neumann and the Heisenberg operators satisfying the Heisenberg equation. For time-dependent generalized oscillators we find the invariant…
In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore…
Using the transformations from paper I, we show that the Schr\"odinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
In this article the time evolution operator of two interacting quantum oscillators, whose Hamiltonian is an element of the complex $\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$ algebra, is analyzed using the Feynman time ordering operator…
We show that the radial harmonic oscillator problem in the position-dependent mass background of the type $m(\alpha;r) = (1+\alpha r^2)^{-2}$, $\alpha>0$, can be solved by using a point canonical transformation mapping the corresponding…
Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator…
For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…
We produce an exact solution of the Schr\"odinger equation for the generalized time dependent Swanson oscillator. The system studied is a non-Hermitian setup characterized by time dependent complex coefficients. The exact solution is…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…
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…
We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a…
We present the general solutions for the classical and quantum dynamics of the anharmonic oscillator coupled to a purely diffusive environment. In both cases, these solutions are obtained by the application of the Baker-Campbell-Hausdorff…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
In the wake of a preceding article \cite{RogUnt06} introducing the Schr\"odinger-Virasoro group, we study its affine action on a space of $(1+1)$-dimensional Schr\"odinger operators with time- and space-dependent potential $V$ periodic in…