Related papers: Airy eigenstates and their relation to coordinate …
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schroedinger-like equation which provides a semiclassical…
Problems posed by semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The…
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the…
This paper gives a constructive answer to the question whether photon states can contain or not, and to what extent, the readings of rulers and clocks. The paper first shows explicitly that, along with the momentum representation, there is…
The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
The aim of this work is to study the Airy and Schr\"odinger operators on looping-edge graphs, a class of metric graphs consisting of a circle and a finite number $N$ of infinite half-lines attached to a common vertex. For the Airy operator,…
Nonlocal terms in the Einstein Hilbert(EH) action appears as IR corrections in effective theory of quantum gravity. Here we have considered such an action keeping the terms which are quadratic in Ricci Scalar. We obtain the solution for a…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
We calculate the uncertainties in the position and momentum of a particle in the 1D potential V(x)=F|x|, F>0, when the position and momentum operators obey the deformed commutation relation [x,p]=i\hbar(1+\beta p^2), \beta>0. As in the…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
We solve exactly the eigenvalue problem for a spin Hamilton operator describing graviton-photon coupling. Entanglement of the eigenstates are also studied. Other spin-coupled Hamilton operators involving spin-1 and spin-2 are also…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
A stochastic Schr\"odinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum…