Completeness Relations for Loss‐Free Microwave Junctions
1.E. P. Wigner, Am. J. Phys. 17, 99 (1949).
2.S. Tomonaga, J. Phys. Soc. (Japan) 2, 158 (1947).
3.S. Tomonaga, J. Phys. Soc. (Japan) 3, 93 (1948).
4.T. Miyazima and T. Tati, J. Sci. Research Inst. (Tokyo) 43, 1 (1949). I am grateful to Professor Tomonaga for sending me this, and several other papers which were not available here.
5.From the notational point of view the similarity is also brought out in some unpublished wartime reports of H. A. Bethe. I am indebted to Dr. H. Motz for bringing these to my attention.
6.E. P. Wigner and L. Eisenbud, Phys. Rev. 72, 29 (1947).
7.T. Teichmann, Ph.D. thesis, Princeton University (1949).
8.T. Teichmann and E. P. Wigner, (to be published).
9.K. Fränz, Elek. Nachr.‐Tech. 21, 8 (1944).
10.J. C. Slater, Revs. Modern Phys. 18, 441 (1946). This reference is particularly adapted to the needs of the present paper. For my own background I am, however, mainly indebted to some unpublished manuscripts of Professor R. H. Dicke and Professor E. P. Wigner.
11.E. P. Wigner (unpublished).
12.H. Weyl, J. f. Math. 143, 177 (1913). The main object of this paper was, however, the derivation of the asymptotic distribution of the proper frequencies of the cavity.
13.Details are given in a forthcoming note by E. P. Wigner and the author; the lack of completeness seems to have been pointed out first by E. P. Wigner in reference 11.
14.See, for example, O. D. Kellog, Foundations of Potential Theory (Verlag. Julius Springer, Berlin, Germany, 1929), p. 246. Details of this, and several of the following results relating to the irrotational part of the field will be found in reference 13.
15.W. Cauer, Gött. Nach. N.F.1 (Fachgruppe I) 1 (1934). In the case of microwave junctions, the non‐irrotational part of Y, i.e., the first term of (2.43) was given by Fränz and by Slater (see reference 10).
16.E. P. Wigner, Phys. Rev. 70, 606 (1946).
17.E. P. Wigner, Phys. Rev. 73, 1002 (1948).
18.T. Teichmann, Phys. Rev. 77, 506 (1950).
19.G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics (Princeton University Press, Princeton, New Jersey, 1951).
20.S. Minakshisundaram and A. Pleijel, Can. J. Math. 1, 242 (1949).
21.H. Weyl, Bull. Am. Math. Soc. 56, 115 (1950).
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