[HN Gopher] The formula for pi buried in a hydrogen atom
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       The formula for pi buried in a hydrogen atom
        
       Author : silasrude
       Score  : 90 points
       Date   : 2020-04-11 21:00 UTC (1 days ago)
        
 (HTM) web link (www.rochester.edu)
 (TXT) w3m dump (www.rochester.edu)
        
       | doovd wrote:
       | The formula is also buried in a simple circle.
        
         | FigmentEngine wrote:
         | no that's tau
        
           | z3ncyberpunk wrote:
           | Tau is just pi * 2
        
       | geoffmunn wrote:
       | I really love the idea that pure mathematics and nature are the
       | same thing. On a philosophical level, our daily lives are the
       | expression of the differences and inefficiencies of our systems
       | compared to an optimal end-state. Also, sometimes I think that
       | religion and science have more in common than people think.
        
       | segfaultbuserr wrote:
       | Original paper:
       | 
       | * Friedmann, T., & Hagen, C. R. (2015). _Quantum mechanical
       | derivation of the Wallis formula for p_. Journal of Mathematical
       | Physics
       | 
       | https://sci-hub.tw/10.1063/1.4930800
       | 
       | The result didn't come from experimental works, it's a pure
       | theoretical derivation for the sake of mathematical physics.
       | 
       | > _The existence of such a derivation indicates that there are
       | striking connections between well-established physics and pure
       | mathematics that are remarkably beautiful yet still to be
       | discovered._
       | 
       | The paper only has three pages - it set up a particular
       | calculation on the energy levels of hydrogen and obtains a limit,
       | thus recovering the Wallis formula for p. If you know QM (I
       | don't), the paper may be a fun read, it's a short and
       | understandable calculation.
        
         | rrss wrote:
         | The preprint is on arxiv too:
         | https://arxiv.org/pdf/1510.07813.pdf
        
         | algon33 wrote:
         | Thanks for the link. You guessed well, it is a fun read.
         | 
         | Its quite satisfying you get the property from the rotational
         | aspect of the QM.
        
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