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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.

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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