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On the quantum mechanical derivation of the Wallis formula for π
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We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for $\pi$. In particular, we demonstrate that not only the Gaussian trial function, used by Friedmann and Hagen, but also the Lorentz trial function can be used to get the Wallis formula. The anatomy of the integrals leading to the appearance of the Wallis ratio is carefully revealed.
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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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