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References
See for example Planck 1932, Pt. 4, Ch. III.
W. Wilson, Phil. Mag. 29, 795 (1915).
A.Einstein, Verh. Deutsche physikalische Gesellschaft 19, 82 (1917).
The necessary indefinite integrals are in Dwight's Tables, but the best way to carry out closed integrals of this kind is by the use of complex variables. It is not only faster when you know how to do it; it also enables more difficult integrals to be done. For the relevant techniques see Sommerfeld 1923, Note 5; Born 1927, App.2; Goldstein 1950, Sec. 9.7.
N.Bohr, Kgl. Danske Vid. Selsk. Skr., nat.-math. Afd., 8. Raekke IV. 1 (1918); reprinted in van der Waerden 1967.
P.O.Vandervoort, Annals of Phys. 12, 436 (1961); A.A.Slutskin, Sov. Phys. JETP 18, 676 (1964). Calculations of this kind are important in the theory of a plasma confined by a slowly varying magnetic field. See Chandrasekhar 1960, p. 48.
M.Born and W. Heisenberg, Z,Physik 16, 229 (1923).
W.Pauli, Ann. d. Physik 68, 177 (1922).
W.Heisenberg, Z. Physik 33, 879 (1925). Translated and annotated in van der Waerden 1967.
Having established this, we can verify that X m α and X m are actually the same in the correspondence limit. See (6.42).
M.Born and P.Jordan, Zeits. f. Physik 34, 858 (1925).
W.Pauli, Nuov. cim. 10, 1176 (1953), Sec. 2.
L. de Broglie, Comptes rendus 177, 107, 148 (1923).
R.P.Feynman, Revs. Modern Phys. 20, 367 (1948).
That wave functions might be constructed in this way was suggested long ago by Dirac, Phys. Z. Sowjetunion 3, 64 (1933), reprinted in Schwinger 1958.
N.Wiener, J.Math. and Phys. 2, 131 (1923). See also S.G.Brush, Revs. Modern Phys. 33, 79 (1961).
A clear and detailed review, with extensive literature references, is D.I.Blochintsev and B.M.Barbashov, Sov. Phys. Uspekhi 15, 193 (1972). See also J.B.Keller and D.W.McLaughlin, Am. Math, Monthly 82, 451 (1975).
For a recent discussion see K.-S. Cheng, J. Math. Phys. 13, 1723 (1972); 14, 980 (1973).
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(1979). Action and phase. In: Classical Dynamics and Its Quantum Analogues. Lecture Notes in Physics, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021211
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DOI: https://doi.org/10.1007/BFb0021211
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