Science

# Mathematical Formula Pi Discovered Deep Within Hydrogen Atoms

Scientists have discovered something amazing. For the first time, scientists have found the equation lurking in the world of physics. It may not sound too terribly exciting, but it reveals a special, previously unknown connection between quantum physics and math.

"I find it fascinating that a purely mathematical formula from the 17th century characterizes a physical system that was discovered 300 years later," Tamar Friedmann, one of the leading researchers and a mathematician at the University of Rochester in the US.

Carl Hagen, a physicist at the University of Rochester, made the discovery while teaching a class on quantum mechanics, explaining to his students how to use a technique called the 'variation principle' to approximate the energy states of a hydrogen atom.

While he was comparing these values to conventional calculations, he observed a tend that he, nor anyone else, had noticed before. He asked Friedmann to assist him in figuring out what the trend was, and it didn't take long before they realized it was a manifestation of pi.

"We weren't looking for the Wallis formula for pi. It just fell into our laps," said Hagen. "It was a complete surprise," added Friedmann. "I jumped up and down when we got the Wallis formula out of equations for the hydrogen atom."

There are plenty of proofs for the Wallis formula for pi, but all proofs have come from the world of mathematics. Never before has it been observed in quantum mechanics.

"This almost seems like magic," writes Kevin Knudson, a maths contributor for Forbes. "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," said Friedmann. "I'm glad we revealed it."