Understanding Heisenberg’s ‘magical’ paper ofJuly 1925: a new look at the calculational details
Ian J. R. Aitchison, David A. MacManus, Thomas M. Snyder
February 1, 2008
Abstract
In July 1925 Heisenberg published a paper [Z. Phys.33879-893(1925)] which ended the period of ‘the Old Quantum Theory’ and ush-ered in the new era of Quantum Mechanics. This epoch-making paperis generally regarded as being difficult to follow, perhaps partly becauseHeisenberg provided few clues as to how he arrived at the results whichhe reported. Here we give details of calculations of the typewhich, wesuggest, Heisenberg may have performed. We take as a specificexampleone of the anharmonic oscillator problems considered by Heisenberg, anduse our reconstruction of his approach to solve it up to second order inperturbation theory. We emphasize that the results are precisely those ob-tained in standard quantum mechanics, and suggest that somediscussionof the approach - based on the direct computation of transition ampli-tudes - could usefully be included in undergraduate courseson quantummechanics.
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