Quantum Mechanical Derivation of the Wallis Formula for $\pi$
Tamar Friedmann, C. R. Hagen
TL;DR
This paper derives the Wallis formula for π using quantum mechanics by analyzing the hydrogen atom spectrum in spaces of various dimensions, providing a novel connection between quantum physics and mathematical constants.
Contribution
It introduces a quantum mechanical derivation of the Wallis formula for π from the hydrogen atom spectrum in arbitrary dimensions, bridging physics and mathematical analysis.
Findings
Wallis formula for π derived from quantum mechanics
Connection established between hydrogen spectrum and π
Method applicable in spaces of any dimension greater than one
Abstract
A famous pre-Newtonian formula for is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
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