TY - JOUR

T1 - On the quantum mechanical derivation of the Wallis formula for π

AU - Chashchina, O. I.

AU - Silagadze, Z. K.

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2017/8/28

Y1 - 2017/8/28

N2 - We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for π. 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.

AB - We comment on the Friedmann and Hagen's quantum mechanical derivation of the Wallis formula for π. 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.

KW - Variational methods in quantum mechanics

KW - Wallis formula

KW - INEQUALITIES

UR - http://www.scopus.com/inward/record.url?scp=85020890586&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2017.06.016

DO - 10.1016/j.physleta.2017.06.016

M3 - Article

AN - SCOPUS:85020890586

VL - 381

SP - 2593

EP - 2597

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 32

ER -