arXiv subjects

Funmi Akintujoye

Publications and source records attributed to Funmi Akintujoye.

2 recordsLinked to original sources

arXiv2016

Exact diagonalization of the $d-$dimensional confined quantum harmonic oscillator

In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.

quant-ph↗

arXiv2015

Explicit matrix representation for the Hamiltonian of the one dimensional \mbox{spin~$1/2$} Ising model in mutually orthogonal external magnetic fields

We derive an explicit matrix representation for the Hamiltonian of the Ising model in mutually orthogonal external magnetic fields, using as basis the eigenstates of a system of non-interacting \mbox{spin~$1/2$} particles in external magnetic fields. We subsequently apply our results to obtain an analytical expression for the ground state energy per spin, to the fourth order in the exchange integral, for the Ising model in perpendicular external fields.

quant-ph↗