Scientists look into hydrogen atom, find old recipe for pi
A duo of scientists have spotted something unexpected in their聽calculations for the energy levels of a hydrogen atom: a 360-year old formula for pi.
Published in 1655 by the English mathematician John Wallis, the Wallis product is an infinite series of fractions that, when multiplied, equal pi divided by 2. It has not appeared in physics at all until now, when聽University of Rochester scientists Carl Hagen and Tamar Friedmann collaborated on a problem set that Dr. Hagen had developed for his quantum mechanics class.聽聽
Instead of using Niels Bohr鈥檚 near-century-old calculations for the energy states of hydrogen, Hagen had his students use a method called the variational principle, just to see what might happen. Ultimately, the calculations demanded mathematical expertise, which came in the form of Dr. Friedmann, who is both a mathematician and a physicist.
鈥淥ne of the things that I鈥檓 able to do is talk to both mathematicians and physicists, and that basically requires translating between two languages,鈥� says Friedmann, who studied mathematics as an undergraduate student at Princeton, where she also earned a PhD. in Theoretical and Mathematical Physics.
Friedmann says that聽asking new questions in math from physics and seeking to understand the physical systems from a mathematical standpoint聽enriched her understanding of problems in both disciplines. Friedmann tends to take on problems that might not even have an answer; she thinks that鈥檚 the type of approach that can lead to new discoveries. 鈥淎nd when they happen,鈥� Friedmann says, 鈥渋t鈥檚 really amazing.鈥�
Hagen and Friedmann聽weren鈥檛 looking for the Wallis formula, rather, they happened upon it while experimenting. As Hagen聽said in a release, 鈥�.鈥�
Friedmann says she聽sees this discovery as a good example of keeping an open mind and letting the research tell you what鈥檚 there. "The special thing is that it brings out a beautiful connection between physics and math,鈥� Friedmann said in a release. 鈥淚 find it fascinating that a purely mathematical formula from the 17th century characterizes a physical system that was discovered 300 years later."
Of course, there has always been a strong relationship between physics and math, in that mathematics provides the language to describe and conduct the work of physics. But it is worth stopping now and again to ponder just聽how amazing it is that聽mathematics, a product of human thought whose rules are derived independently of any experience, can describe so neatly and precisely the physical world, a phenomenon that聽Nobel Prize-winning physicist聽Eugene Wigner called, in聽a 1959 lecture,聽the "," which he characterized聽as "a聽wonderful gift which we neither understand nor deserve.鈥澛�
[Editor's note: Because of an editing error, an earlier version of this article聽尘颈蝉蝉辫别濒濒别诲听Eugene Wigner's name.]
