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Quasiclassical approximation with the centrifugal potential excluded

  • Atoms, Spectra, Radiation
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Abstract

We develop a modification of the WKB method (the modified quantization method, or MQM) for finding the radial wave functions. The method is based on excluding the centrifugal potential from the quasiclassical momentum and changing correspondingly the phase in the Bohr-Sommerfeld quantization condition. MQM is used to calculate the asymptotic coefficients at zero and at infinity. We use the examples of power-law and funnel potentials to show that MQM not only dramatically broadens the possibilities of studying the energy spectrum and the wave functions analytically but also ensures accuracy to within a few percent even when one calculates states with a radial quantum number n r ∼1, provided that the angular momentum l is not too large. We also briefly discuss the possibility of generalizing MQM to the relativistic case (the spinless Salpeter equation).

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Authors and Affiliations

  1. Moscow Engineering Physics Institute (Technical University), 115409, Moscow, Russia

    B. M. Karnakov & V. D. Mur

  2. Institute of Theoretical and Experimental Physics, 117259, Moscow, Russia

    V. S. Popov

Authors
  1. B. M. Karnakov
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  2. V. D. Mur
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  3. V. S. Popov
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Additional information

Zh. Éksp. Teor. Fiz. 116, 511–525 (August 1999)

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Karnakov, B.M., Mur, V.D. & Popov, V.S. Quasiclassical approximation with the centrifugal potential excluded. J. Exp. Theor. Phys. 89, 271–278 (1999). https://doi.org/10.1134/1.558980

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  • DOI: https://doi.org/10.1134/1.558980

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