The notorious numberPihas come through in becoming even more rife in scientific discipline . Researchers from the University of Rochester discovered that a formula which judge the energy levels of a atomic number 1 atom is the same as the one develop 360 years ago by English mathematician John Wallis to find the value of Pi .
The span of physicist realized that when the variational method was employed to calculate the energy levels of the hydrogen atoms , the formula could be simplified into theWallis Product , the one used for Pi .
The variational method acting is used to estimate the crushed vigour country of speck , when the negatron are close to the cell nucleus . It is not usually used on the atomic number 1 atom , as hydrogen is uncomplicated enough so scientist can compute the push levels precisely . Energy levels give an indication of how tightly bound the negatron is to an speck ; the prominent the Department of Energy degree , the easy it is for the electron to break free .
Professor Carl Hagen was teaching his scholarly person how to use the variational method acting and used the hydrogen speck as an example in the explanation . The students had to calculate the expected values using the variational method acting and compare it with the exact root and then cipher the error in the approximation .
When Hagen begin to lick the job he insure an unusual trend emerging . The errors were getting small-scale as the energy level grew larger , which was surprising as the variational method only give a near approximation for the modest zip levels .
Hagen raise Tamar Friedmann to study what would happen to the approximation as the DOE increase , and they discovered that the formula was exactly the Wallis Product .
" It was a complete surprisal – I leap up and down when we got the Wallis formula out of equations for the hydrogen speck , " say Friedmann in astatement . " The special thing is that it brings out a beautiful connection between physics and math . I find it fascinating that a strictly mathematical formula from the 17th century characterise a physical system that was discovered 300 geezerhood subsequently . "
The paper discussing the find is only three pages long and has been issue in theJournal of Mathematical Physics .
Top Image Credit : Pi by J.Gabás Esteban , via Flickr . cubic centimetre BY 2.0