Researchers, for the first time ever, have found a classic formula for pi concealed in the world of quantum physics. Everybody is aware of the word pi. It is the ratio among a circle’s circumference and its diameter, and is very vital in pure mathematics, but now scientists have also discovered it “lurking” in the world of quantum physics, while using quantum mechanics to link the energy levels of a hydrogen atom. So why is that even exciting? Well, it reveals an exceedingly special and previously unknown connection among 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 300 years later.
Carl Hagen, a particle physicist presently working at the University of Rochester, found this interesting connection while coaching a class on quantum mechanics and clarifying to his pupils how to utilize 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 a rare trend in the ratios. So he asked Friedmann to help him work out this trend, and they rapidly understood that it was fundamentally an appearance of the Wallis formula for pi – the first time it had even been in fact derived from physics.
Since 1655 there have been lots of confirmations of Wallis’s formula, but they all have come from the territory of mathematics, and the new conclusions have people stunned. The results have been issued in theJournal of MathematicalPhysics.
Two pages from Wallis’s book Arithmetica Infinitorum Digitised by Google
Maths contributor Kevin Knudson for Forbes, wrote “This almost looks 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.