475 citations
7 papers
Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field
M. G. Naber
The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes…
The Zeta Function for the Triangular Potential
M. G. Naber
The zeta functions for the Schrödinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization the…
The Bessel zeta function
M. G. Naber, B. M. Bruck, S. E. Costello
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkin…
Linear Fractionally Damped Oscillator
Mark Naber
In this paper the linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considere…
Time fractional Schrodinger equation
Mark Naber
The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamil…
Distributed order fractional sub-diffusion
Mark Naber
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative…