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On the Quantum Theory of Vibration-Rotation Bands

  • J. R. Oppenheimer
Extract

The dynamical problem of the “diatomic molecule” is solved on the new mechanics. The terms of the rotational energy are , where ; the weights of the corresponding states are 2m; the frequencies differ a little from the classical ones. Finally the intensities are slightly different from those computed by Kemble; the main term agrees with that of Fowler, but the positive branch is only slightly stronger than the negative. The central line vanishes. The intensities are valid only for the fundamental band.

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* Fowler, , Phil. Mag. vol. XLIX, p. 1272 (1925).

Kemble, , Phys. Rev. vol. xxv, p. 1 (1925).

Dirac, , Proc. Roy. Soc. A, vol. cx, p. 561 (1926); Born, , Heisenberg, , Jordan, , Zeit. f. Physik, vol. xxxv, p. 557 (1926).

§ Brillouin, , C.R. vol. CLXXXII, p. 374 (1926).

| Heisenberg, , Zeit. f. Physik, vol. xxx, p. 879 (1925); Born, und Jordan, , Zeit. f. Physik, vol. xxxiv, p. 858 (1925).

* Dirac, , Proc. Roy. Soc. A, vol. cx, p. 561 (1926).

Kemble, , Phys. Rev. vol. xxv, p. 1 (1925).

Heisenberg, , Zeit. f. Physik, vol. XXXIII, p. 879 (1925); Born, und Jordan, , Zeit. f. Physik, vol. xxxiv, p. 858 (1925).

* Dirac, , Proc. Roy. Soc. A, vol. cx, p. 561 (1926); Born, , Heisenberg, , Jordan, , Zeit. f. Physik, vol. xxxv, p. 557 (1926).

Dirac, , Proc. Roy. Soc. A, vol. cxi, p. 281 (1926).

Born, , Atommechanik, § 20.

* Dirac, , Proc. Roy. Soc. A, vol. cxi, p. 281 (1926).

Dirac, , Proc. Roy. Soc. A, vol. cx, p. 561 (1926); Born, , Heisenberg, , Jordan, , Zeit. f. Physik, vol. xxxv, p. 557 (1926).

* On Schrodinger's Theory there is no normal state for a rigid rotator in two dimensions, and the transitions for m, (½→½), (−½→½) occur.

* Kemble, , loc.cit. and Fowler , Phil. Mag. vol. L, p. 1079 (1925).

For the fundamental hydrogen chloride band studied by Kemble and Fowler the values of 4γ and differ by only about 10 per cent.; the positive branch remains slightly the stronger.

* Schrödinger, , Ann. A. Phys. vol. LXXIX, p. 484 (1926). See particularly Eq. (51).

Mensing, , Zeit. f. Physik, vol. xxxvi, p. 814 (1926).

Born, und Jordan, , Zeit. f. Physik, vol. xxxiv, p. 838 (1925).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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