Related papers: Toroidal moments of Schr\"odinger eigenstates
A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is…
Spectral singularities such as exceptional points invoke specific physical effects. The present paper focuses upon the time dependent solutions of the Schr\"odinger equation. In a simple model it is demonstrated that - depending on initial…
Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We…
The effective dynamics of solitons for the generalized nonlinear Schr\"odinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton,…
A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
The work deals with one of the topics of collective motion. In the frame of Nuclear Fluid Dynamics, a model which portrays the nuclear matter as a quantum elastic body, the torus-like motions and their associated energies are computed using…
Small perturbations of ideal turbulence obey the Schrodinger equation. Microscopically, the perturbation of turbulence corresponds to formation of small amplitude helices on straight vortex filaments. A helix behaves in the vorticity field…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
A reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q twisted by the ell-th Hecke eigenvalue as the fourth moment of automorphic L-functions of level ell twisted by the q-th Hecke…
We investigate the particle production in a toroidal compactified spacetime due to the expansion of a Friedmann cosmological model in R3 x S1 outside a U(1) local cosmic string. The case of a Friedmann spacetime is also investigated when…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…
For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that…
We have developed a formalism to get the time evolution of the eigen states of Rindler Hamiltonian in momentum space. We have shown the difficulties with characteristic curves, and re-cast the time evolution equations in the form of…
This work provides a comprehensive numerical characterization of the excited spherically symmetric stationary states of the Schr\"odinger-Poisson problem. Through numerical computation of highly excited eigenstates, novel heuristic laws are…
Bohmian trajectories on the toroidal surface T^2 are determined from eigenfunctions of the Schrodinger equation. An expression for the monodromy matrix M(t) on a curved surface is developed and eigenvalues of M(t) on T^2 calculated.…
In this paper the nodal structure for He atom is revisited and a procedure for identifying the symmetry properties and nodal structure of the time and spin independent Schroedinger equation will be presented. Application are made to the few…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
We consider the 3D cubic nonlinear Schr\"odinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of global solutions to the time-dependent model can be described…