A standard formula for Pi (π) was discovered hidden in hydrogen atoms

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This happened two years ago ... It was a spectacular discovery.
Back in 2015, scientists found something amazing for the first time, a standard version of Pi that is hidden in the folds of quantum mechanics.
pi is a ratio between the circumference of the circle and its diameter, which is very important in pure mathematics, but this is the first time that scientists discover this percentage looming in the folds of physics, and discovered when using quantum mechanics to compare energy levels of a hydrogen atom.
Why was this discovery exciting? Well, this discovery has shown a special kind of connection that was not previously known between quantum physics and mathematics.
"I found it wonderful that a purely mathematical formula from the seventeenth century appears in a physical system discovered three hundred years later," said Tamar Friedman, a mathematics scientist at the University of Rochester and one of the leaders of the research.
The discovery was made when Karl Hagen, a physicist at the University of Rochester, gave a lesson on quantum mechanics and explained to his students how to use a mechanical technique known as the "deviation principle" to approach energy levels of a hydrogen atom. When comparing these values ​​with the reference calculations, An unusual trend in calculated proportions.
Hagen requested the help of his colleague Tamar Friedman to see this trend, and they quickly realized that this was an explanation of the Wallis formula for Pi, and this is the first time that this percentage of physics fields has been extracted.
"We were not looking for the Wallis formula for Pi but it came up in our research," says Hagen. "It was a complete surprise, I was shocked that I jumped in my place when we got the Wallis formula of hydrogen atom equations."
Since 1655 there have been several proofs of the Wallis formula, but before that, all of these proofs came from the branches of mathematics, you can see two pages of the book Wallis (small account) title of the book in Latin Arithmetica Infinitorum.

"It looks like magic," wrote sports expert Kevin Knudson of Forbes. "Finding the formula for the ratio مخ hidden in the quantum mechanics of a hydrogen atom is a pleasant and surprising thing."
"Nature has hidden this secret for the last 80 years, and I'm glad we've discovered it," says Friedman.
We can only imagine what other secret links are between quantum mechanics and pure mathematics.
The results were published in the journal Mathematical Physics.
Source : Aip.Scitation

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