A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular exam...

In this article we describe a numerical method to solve a nonhomogeneous diffusion equation with arbitrary geometry by combining the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunction expansion method (EEM). This forms a meshless numerical scheme of the MFS-MPS-EEM model to solve nonhomogeneous diffusion equations with time-independent source ...

0885–3010/$25.00 © 2014 IEEE Abstract—Across a range of spectral estimation problems and beam focusing problems, it is necessary to constrain the properties of a function and its Fourier transform. In many cases, compact functions in both domains are desired, within the theoretical bounds of the uncertainty principle. Recently, a hyperbolic sine function of modified argument and power was found...

the series on the right of (3) being called the Fourier Eigenfunction Series and a. the Fourier Coefficients of f(x, y). I have studied elsewhere' the problem of convergence and summability of a Fourier Eigenfunction Series. In this note I am interested in announcing a result on uniqueness of eigenfunction expansion. Actually, we have thfe following, THEOREM. Let us suppose we are given an eige...

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stablished results.

We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Padé method. This approach is based on a rational approximation to a modified logarithmic derivative of the eigenfunction and produces sequences of roots of Hankel determinants that converge towards the eigenvalues of the equation.

This paper extends work of Shen and Walter and others concerning relationships between sampling and time-frequency localization. We consider approximate projections onto eigenspaces of timeand bandlimiting operators, expressed in terms of samples of bandlimited functions. We establish error estimates of eigenfunction samples and on matrices that can be used to generate approximations of these s...