arXiv subjects

V. Oguri

Publications and source records attributed to V. Oguri.

4 recordsLinked to original sources

arXiv2015

Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\geq 4$?

The relativistic hydrogen atom in an Euclidean space-time of arbitrary number of space dimensions ($D$) plus one time dimension is revisited. In particular, numerical solutions of the radial Dirac equation for a generalized Coulombian potential proportional to $1/r^{(D-2)}$ are investigated. It is argued that one could not find any physical solution for $D\geq 4$.

quant-ph↗

arXiv2014

Numerov numerical method applied to the Schrödinger equation

In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is given and, in the sequel, it is applied to two quantum non-relativistic problems with well known analytical solutions: the simple harmonic oscillator and the hydrogen atom. The numerical results are compared to those obtained analytically.

quant-ph↗

arXiv2013

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun Equation

The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigeinfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field.

quant-ph↗

arXiv2013

Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$. The only possible states correspond to $l=0$. How the result depends on the topological mass of the photon is also discussed. In the case $n=1$, the energy of the fundamental state corresponding to different choice for the photon mass scale are found to be comprehended in the interval $-3,5 \times 10^{-3} eV \leq E \leq -9,0 \times 10^{-2} eV$, corresponding to a mean radius of the electron in the range $ (5.637 \pm 0.005) \times 10^{-8}$~cm $\leq \leq (48.87 \pm 0.03) \times 10^{-8}$~cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.

quant-ph↗