Related papers: Exact solutions for time-dependent complex symmetr…
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…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
There exist a number of typical and interesting systems or models which possess three-generator Lie-algebraic structure in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator…
We study the Non-Hermitian quantum mechanics for the discrete system. This paper gives an exact analytic single-particle solution for an $N$-site tight-binding chain with two conjugated imaginary potentials $\pm i\gamma $ at two end sites,…
In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl…
The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present…
We discuss the relationship between exact solvability of the Schr\"{o}dinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The…
We study the time-dependent Schr\"odinger operator $P = D_t + \Delta_g + V$ acting on functions defined on $\mathbb{R}^{n+1}$, where, using coordinates $z \in \mathbb{R}^n$ and $t \in \mathbb{R}$, $D_t$ denotes $-i \partial_t$, $\Delta_g$…
In this note we investigate local properties for microlocally symmetrizable hyperbolic systems with just time dependent coefficients. Thanks to Paley-Wiener theorem, we establish finite propagation speed by showing precise estimates on the…
This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and…
Solutions of the time-dependent Schr\"odinger equation are mapped to other solutions for a (possibly) different potential by so-called form-preserving transformations. These time-dependent transformations of the space and time coordinates…
We propose a procedure to obtain exact analytical solutions to the time-dependent Schr\"{o}dinger equations involving explicit time-dependent Hermitian Hamitonians from solutions to time-independent non-Hermitian Hamiltonian systems and the…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
Fredholm integral operators that commute with the Hamiltonians of certain quantum mechanical problems with quartic potentials are introduced. The operators are expressed in terms of an Airy function, and their eigenvalues fall off…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
We investigate the distribution of work performed on a Brownian particle in a time-dependent asymmetric potential well. The potential has a harmonic component with time-dependent force constant and a time-independent logarithmic barrier at…
The common treatment of time-dependent potentials, such as those used for radio frequency cavities, is to average a potential's time component through the interval that the reference particle spends in the cavity. Such an approach, using…
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines…