Approximate solution of the strongly magnetized hydrogenic problem with the use of an asymptotic property

Details Approximate solution of the strongly magnetized hydrogenic problem with the use of an asymptotic property Approximate solution of the strongly magnetized hydrogenic problem with the use of an asymptotic property

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983phrva..28.2071r&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 28, Oct. 1983, p. 2071-2077. Research supported by the De

Physics

General Physics

17

Asymptotic Methods, Electron States, Field Strength, Quantum Mechanics, Stellar Magnetic Fields, Approximation, Hydrogen, Quantum Numbers, Thermodynamic Equilibrium

Scientific paper

It is shown that the effective potentials of the adiabatic approximation, which depend on the magnetic field parameter (beta = B/Bzero) and the quantum number (s = -m is zero or greater) of the z component of the angular momentum, can be asymptotically traced back to one single potential function which depends solely on the ratio p = beta/(s + 1/2). For this asymptotic potential, numerical solutions of the Schroedinger equation are determined in the range of p = 0.001-1000 where the number v of nodes of the longitudinal wave function is 0-20. Exploiting the concept of quantum excesses, the asymptotic energies are extrapolated to v greater than 20. It is found that the asymptotic energies provide the energy values of the real physical problem of hydrogenic atoms in magnetic fields of beta greater than about one within an accuracy of less than above one percent for every (s = three or more) and arbitrary v.

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