Zur Theorie des Wasserstoffatoms in Zeitschrift für Physik, Band 99, Heft 7 & 8, March 1936, pp. 576-582
Berlin: Julius Springer, 1936. 1st Edition. FIRST EDITION IN ORIGINAL PRINTED WRAPS OF BARGMANN’S RELATION OF FOCK’S “GLOBAL METHOD” OF TREATMENT FOR THE HYDROGEN ATOM TO THE “INFINITESIMAL METHOD” OF PAULI (Chattargi, The Theory of Auger Transitions, 36; Avery, Applications in Quantum Theory, xii). Note that we offer the Fock paper separately. A German-American theoretical physicist and mathematician, Valentine ‘Valya’ Bargmann worked as an assistant to Albert Einstein at Princeton from 1937-1946.
In this paper, Bargmann shows “that a group theoretical interpretation of the matrix equations that Pauli used as a basis of his treatment of the hydrogen atom leads to the method recently developed by Fock. The separation of the Schrödinger equation in parabolic coordinates will be introduced in this connection” (Bargmann, 1936, 576).
“In a very interesting paper, Fock reduces the Schrödinger equation of the hydrogen atom in momentum space to an integral equation in the spherical harmonics in four variables, by making a stereographic projection between momentum space and the four dimensional unit sphere. These considerations are [as Bargmann shows] closely connected with the treatment of the hydrogen atom by the matrix calculus of Pauli. The group theoretical interpretation of the relations derived by Pauli lead necessarily to Fock’s method” (ibid).
Bargmann draws “the connection between Fock’s analytic approach and Pauli’s algebraic approach [six months after Fock’s paper when he noticed that the operators L and M in Pauli’s article functioned as the generators of infinitesimal rotations of the four-dimensional hypersphere, giving rise to the SO (4) group as outlined by Fock. Since the angular momentum components were known to generate the familiar three-dimensional rotation group SO (30, the components of the LRL vector were deemed responsible for the additional symmetry and accidental degeneracy of the hydrogen atom” (ibid).
In addition to his work with Einstein, Bargmann also collaborated “with the mathematician John von Neumann on work that was to help lead to the development of computers” (NYTimes Obituary, 25 July 1989). Item #949
CONDITION & DETAILS: Complete issue. 8vo. 9 x 6 inches; 225 x 140mm). Very slight toning at the edges of the wraps and interior (the scanner makes it appear much, much darker in the image than to the naked eye). Front wrap is detached; very slight chipping of the paper at the spine; withal bright, clean, and in very good to near fine condition.