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Quantum Mechanical Derivation of the Wallis Formula for π
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🧮 math-ph
math.MPmath.NTquant-ph
keywords
dimensionsformulaapproacharbitraryatomderivationdirectlyfamous
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A famous pre-Newtonian formula for $\pi$ 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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Forward citations
Cited by 2 Pith papers
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Emergence of $\pi$ from Equatorial Quantum Localization
A natural geometric rigidity index for equatorial localization on the sphere in highest-weight spherical harmonics is exactly a Wallis partial product, recovering π via the correspondence principle in the large-quantu...
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Quantum Realization of the Wallis Formula
Quantum states in the 3D harmonic oscillator and planar Fock-Darwin systems realize the Wallis formula for pi through the scale-independent observable Q = <r><r^{-1}> that approaches 1 at high angular momentum.
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