Physics. — "A remarkable case of quantization.'" Bj Prof. P. 

 Ehrknfest and G. Brkit. 



(Communicated at the meeting of January 28, 1922). 



1. It is possible to indicate simple mechanical systems for which 

 a formal apj)lication of the quantum rules gives well defined and 

 jed apparently unreasonable stationary motions. Bohr's Principle of 

 Correspondence') ofïers an essentially new viewpoint for the treat- 

 ment of these cases and will probably contribute to their complete 

 solution. It will suflice to discuss a special case which is so chosen 

 as to minimize the mathematical analysis. ') 



2. A rigid electric dipole having a moment of inertia / is free 

 to rotate in the A^, Y plane about its own midpoint. 



Let us suppose that by means of a suitable kinematical arrange- 

 inent (he rotating dipole is thrown back elastically as soon as the 

 aijgle (p, which the dipole makes with the axis of A, reaches the 

 boundaries of the interval 



— ƒ. 2jr^r/)^ + /.2jr ....... (1) 



where / is a large, in general an irrational number. Let an angular 

 velocity to be given to the dipole. Its angular momentum is then 

 p =: lo) and it executes a periodic motion with the period 



T = ^f.— (2) 



w 



During the motion the dipole traverses the interval (J) making 

 in a period 2/ complete revolutions to the right followed by the 

 same number of revolutions to the left. In the motion the "quasi- 

 periode" 



^) N. Bohr, Quantum theory of line-spectra f, II Kopenhagen 1918. H. Kramers, 

 Intensities of spectral lines. Kopenhagen 1919. 



2) A case which differs slightly from the one discussed in § 2, namely the case 

 of a rigid dipole torsionally suspended by an elastic thread of small rigidity one 

 of us submitted to Einstein for consideration as early as 1912 (with reference to 

 the problem of quantization of H^ molecules — P. Ehrenfest. Verb. d. D. Phys. 

 Ges. 15, 451, 1913). It was impossible however to settle the difffculty here discussed 

 -by the means which were then available. 



