Related papers: Existence of Time Operator for a Singular Harmonic…
In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is…
A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
The eigenstates of linear combinations of the Susskind and Glogowerphase operators for the harmonic oscillator are constructed. It is shown that such eigenstates are squeezed states.
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…
The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). In this paper,…
This thesis explores the concept of realizing quantum gates using physical systems like atoms and oscillators perturbed by electric and magnetic fields. The basic idea is that if a time-independent Hamiltonian $H_0$ is perturbed by a…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time…
In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such…
A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator…
The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.
Effective Liouville operators of the first- and the second-order symplectic integrators are obtained for the one-dimensional harmonic-oscillator system. The operators are defined only when the time step is less than two. Absolute values of…
Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically,…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact…
We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions.…
A variety of coherent states of the harmonic oscillator is considered. It is formed by a particular superposition of canonical coherent states. In the simplest case, these superpositions are eigenfunctions of the annihilation operator…