Abstract

The process of simultaneous emission of two photons (of continuous probability distribution in energy) in the transition from one discrete quantum level to another is here analyzed in the correspondence principle limit in which the quantum numbers of the two states are large and the change in quantum number is small by comparison. In this limit, it proves possible to define a classical dynamical quantity [Eq. (19)], the frequency analysis of whose classical variation with time in a definite orbit determines in the given approximation the absolute transition probability and intensity distribution in the continuous spectrum in question.

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  1. G. Breit and E. Teller, Astrophys. J. 91, 215 (1940). Note added in proof: Eq. (2) predicts a transition probability smaller by a factor 2π than that given by Breit and Teller. To date the source of the discrepancy has not been located.
  2. Here and below we use ω to designate circular frequency, in units radians per sec.; and use hℏ to represent the quantum of angular momentum (1.027×10-27 g cm2/sec.) as distinct from the quantum of action, h.
  3. For a discussion of the correspondence principle in the light of wave mechanics see, for example, H. A. Kramers, Quantentheorie des Elektrons und der Strahlung (Akademische verlagsgesellschaft, Leipzig, 1938), Vol. II, Section 85, also appears in Vol. I, Part II of Hand- und Jahrbuch der Chemischen Physik. For a correspondence principle treatment of double-photon processes before the period of wave mechanics, see H. A. Kramers and W. Heisenberg, Zeits. f. Physik 31, 681 (1925). For a wave-mechanical analysis, see M. Goeppert Mayer, Ann. d. Physik 9, 237 (1931).
  4. See, for example, Ruark and Urey, Atoms, Molecules and Quanta (McGraw-Hill Book Company, Inc., New York, 1930), p. 585.

Breit, G.

G. Breit and E. Teller, Astrophys. J. 91, 215 (1940). Note added in proof: Eq. (2) predicts a transition probability smaller by a factor 2π than that given by Breit and Teller. To date the source of the discrepancy has not been located.

Kramers, H. A.

For a discussion of the correspondence principle in the light of wave mechanics see, for example, H. A. Kramers, Quantentheorie des Elektrons und der Strahlung (Akademische verlagsgesellschaft, Leipzig, 1938), Vol. II, Section 85, also appears in Vol. I, Part II of Hand- und Jahrbuch der Chemischen Physik. For a correspondence principle treatment of double-photon processes before the period of wave mechanics, see H. A. Kramers and W. Heisenberg, Zeits. f. Physik 31, 681 (1925). For a wave-mechanical analysis, see M. Goeppert Mayer, Ann. d. Physik 9, 237 (1931).

Teller, E.

G. Breit and E. Teller, Astrophys. J. 91, 215 (1940). Note added in proof: Eq. (2) predicts a transition probability smaller by a factor 2π than that given by Breit and Teller. To date the source of the discrepancy has not been located.

Other

G. Breit and E. Teller, Astrophys. J. 91, 215 (1940). Note added in proof: Eq. (2) predicts a transition probability smaller by a factor 2π than that given by Breit and Teller. To date the source of the discrepancy has not been located.

Here and below we use ω to designate circular frequency, in units radians per sec.; and use hℏ to represent the quantum of angular momentum (1.027×10-27 g cm2/sec.) as distinct from the quantum of action, h.

For a discussion of the correspondence principle in the light of wave mechanics see, for example, H. A. Kramers, Quantentheorie des Elektrons und der Strahlung (Akademische verlagsgesellschaft, Leipzig, 1938), Vol. II, Section 85, also appears in Vol. I, Part II of Hand- und Jahrbuch der Chemischen Physik. For a correspondence principle treatment of double-photon processes before the period of wave mechanics, see H. A. Kramers and W. Heisenberg, Zeits. f. Physik 31, 681 (1925). For a wave-mechanical analysis, see M. Goeppert Mayer, Ann. d. Physik 9, 237 (1931).

See, for example, Ruark and Urey, Atoms, Molecules and Quanta (McGraw-Hill Book Company, Inc., New York, 1930), p. 585.

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