Scientists, for the first time ever, have discovered a
classic formula for pi hiding in the world of quantum physics. Everybody is
familiar with the word pi. It is the ratio among a circle's circumference and
its diameter, and is extremely vital in pure mathematics, but now researchers
have also found it "lurking" in the world of quantum physics, while
using quantum mechanics to compare the energy levels of a hydrogen atom.

So why
is that even exciting? Well, it discloses an extremely special and previously
unidentified connection between quantum physics and mathematics. It is quite
interesting that a purely mathematical formula from the early 17th century
portrays a physical system that was discovered 400 years later.

Image Credit: Benjamin Haas/Shutterstock.com |

Carl Hagen, a particle physicist currently working at the
University of Rochester, discovered this interesting connection while teaching
a class on quantum mechanics and clarifying to his pupils how to use a quantum
mechanical method identified as the 'variation principle' to estimate the
energy states of a hydrogen atom. So while comparing these values to
conventional calculations, Carl Hagen noticed an uncommon trend in the ratios.
So he asked Friedmann to assist him work out this trend, and they rapidly
realized that it was essentially an appearance of the Wallis formula for pi –
the first time it had even been actually derived from physics.

Since 1655 there have been lots of verifications of Wallis's
formula, but they all have come from the realm of mathematics, and the new
outcomes have people stunned. The outcomes have been issued in the Journal of
Mathematical Physics.

Two pages from Wallis's book Arithmetica Infinitorum Digitised by Google |

Maths contributor Kevin Knudson for Forbes, wrote "This
almost seems like magic. That a formula for π is hidden inside the quantum
mechanics of the hydrogen atom is surprising and delightful."

“Nature had kept this secret for the last 80 years. I'm glad
we revealed it." said Friedmann.

We just can't help but wonder what other secret links are
prowling between quantum mechanics and pure mathematics.

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