. The Bell System technical journal . fore is the onlyorbit for which the energv-value and the angular momentum of theatom are simultaneously equal to —Rh and to /; 2ir we admit the ellipses to equal value with the circle, we concedethat the equality of the angular momentum with /; 2;r is of no sig-nificance. There is a partial escape from this conclusion for the remainingstationary- states. Take for instance the second, of energy-value— Rh, 4. The circular orbit of diameter 4eE Rh, for which the atompossesses this energy-value, is distinguished by the angular momen-tum 2/j 2t.
. The Bell System technical journal . fore is the onlyorbit for which the energv-value and the angular momentum of theatom are simultaneously equal to —Rh and to /; 2ir we admit the ellipses to equal value with the circle, we concedethat the equality of the angular momentum with /; 2;r is of no sig-nificance. There is a partial escape from this conclusion for the remainingstationary- states. Take for instance the second, of energy-value— Rh, 4. The circular orbit of diameter 4eE Rh, for which the atompossesses this energy-value, is distinguished by the angular momen-tum 2/j 2t. For each of the infinity of ellipses possessing the samemajor axis 4eE/Rh there is a different value of the angular momentum; 672 BELL SYSTEM JOURXAL hut ilicre is one among them for which the angular momentum isequal to /; 2-k. And in general for the wth stationary state of energy-value — Rh ir. there are « elliptical (including one circular) orbitswhich would give the same cnerg>-\alue and ;; \alues of angular. 9., 16a, Fig. 4a—Diagram to show the proportional dimensions of ellipses with identicaltotal quantum-number « = / 7; and different azimuthal quantum-numbers * = 1,2 .... n ! rom left to right we have the cas?s « = 1, 2, 3, 4, on scales varying asindicated by the subjoined arrows. momentum equal rcspecti\eK to nli Itt, {ii — l)li 2ir Iilir. These, as the reader can show from (.)2). are distingtiished by thefollowing values of t: E- =k n k = \. (o3) Thus if we desire to regard the equalit\- of angular momentum withan integer multiple of h 2-k as being essential to the permissible orbits,we can keep, along with the circles, some of the other elliptical orbitscompatible with tiie prescribed energ>-\ allies; btit except for these
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