Year: 2025
Type: article
Abstract: We demonstrate the time evolution of a free particle in three dimensions when the initial condition is an arbitrary radial function f(r). The solution is expressed as a series expansion in terms of generalized Bessel functions derived using a 3D recursion formula for Bessel functions in the radial coordinate r. Additionally, we establish that these generalized Bessel functions can be represented through intricate double series, which ultimately enable the construction of the full solution. This work presents a novel solution to the problem, as previous approaches were limited to expressions involving only spherical Bessel functions.
Source: Axioms
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4416665096