Related papers: Formula Method for Bound State Problems
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
The instantaneous formulations for the relativistic Bethe-Salpeter (BS) and the radiative transitions between the bound-states are achieved if the BS kernel is instantaneous. It is shown that the original Salpeter instantaneous equation set…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
A systematic method of analysing Bethe-Salpeter equation using spectral representation for the relativistic bound state wave function is given. This has been explicitly applied in the context of perturbative QCD with string tension in the…
The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique…
We consider the focusing wave equation outside a ball of $\R^3$, with Dirichlet boundary condition and a superquintic power nonlinearity. We classify all radial stationary solutions, and prove that all radial global solutions are…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…
In this paper the quantum hydrodynamic equation describing the collective, low energy excitations of a dilute atomic Bose gas in a given trapping potential is investigated with the JWKB semiclassical method. In the case of spherically…
We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main new…
We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be…
We show that the energy of classical solutions to the wave equation with hyperbolic boundary condition (i.e., dynamic Wentzell boundary condition) and damping on the boundary decays like 1/t. In fact we allow mixed boundary conditions: a…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article…
We constrain the possible bound-state solutions of the spinless Salpeter equation (the most obvious semirelativistic generalization of the nonrelativistic Schr\"odinger equation) with an interaction between the bound-state constituents…