7 citations · 13 across the 8 of their papers we have counts for
8 papers
A Modern Functional Analytic Tour of the Fourier-Bessel Transform
Cameron L. Williams
In this paper, we review the theory of the Fourier--Bessel transform. The Fourier--Bessel transform is an integral transform on the half-line that generalizes the Fourier cosine tr…
From the Harmonic Oscillator to Time-Frequency Analysis of Chirp Signals
Donald J. Kouri, Caleb Broodo, Bernhard G. Bodmann +1
This paper presents a novel approach to understanding the role of harmonic dynamics and gaining a deeper appreciation for its impact within and outside of quantum mechanics. This i…
Segal-Bargmann Transforms Associated to a Family of Coupled Supersymmetries
Cameron L. Williams
The Segal-Bargmann transform is a Lie algebra and Hilbert space isomorphism between real and complex representations of the oscillator algebra. The Segal-Bargmann transform is usef…
Point Transformations and the Relationships Among Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem
Donald J. Kouri, Nikhil N. Pandya, Cameron L. Williams +2
We present new connections among anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem. This is done by defining a point transformation to a new position va…
Generalized Fourier transform method for nonlinear anomalous diffusion equation
Jie Yao, Cameron L. Williams, Fazle Hussain +1
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law d…
Coupled Supersymmetry and Ladder Structures Beyond the Harmonic Oscillator
Cameron L. Williams, Nikhil N. Pandya, Bernhard G. Bodmann +1
The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanic…
Canonical Quantization, Quasi-Hermiticity, Observables and the Construction of Complete Basis Sets
Donald J. Kouri, Cameron L. Williams, Nikhil Pandyaq
We consider the problem of designing a variety of "system guided" basis sets for quantum mechanical anharmonic oscillators. Using ideas based on supersymmetric quantum mechanics, w…
Fourier and Beyond: Invariance Properties of a Family of Integral Transforms
Cameron L. Williams, Bernhard G. Bodmann, Donald J. Kouri
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative view…