Wallis formula from the harmonic oscillator
Mathematical Physics
2018-03-14 v2 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We show that the asymptotic formula for , the Wallis formula, that was related with quantum mechanics and the hydrogen atom in \cite{HF}, can also be related to the harmonic oscillator using a quantum duality between these two systems. As a corollary we show that this very interesting asymptotic formula is not related with the hydrogen atom or quantum mechanics itself but with a clever choice of a trial function and a potential in the Schroedinger equation when we use the variational approach to calculate the ground state energy associated with the given potential function.
Keywords
Cite
@article{arxiv.1709.01214,
title = {Wallis formula from the harmonic oscillator},
author = {Ignacio Cortese and J. Antonio García},
journal= {arXiv preprint arXiv:1709.01214},
year = {2018}
}
Comments
v1:8 pages; v2: reference added, typos corrected