S Barcza 2005 J. Phys. A: Math. Gen. 38 2469 doi:10.1088/0305-4470/38/11/009
S Barcza
Show affiliationsBy using the angular oblate spheroidal functions as basis functions a bounded wavefunction is constructed in the singularities of the Schrödinger equation of the diamagnetic Coulomb problem with infinite nuclear mass. The expansion in terms of these functions is a model to resolve singularities in an eigenvalue problem of non-separable partial differential equations of non-relativistic quantum mechanics. A comprehensive asymptotic analysis reveals the complete set of asymptotic solutions, makes possible a uniform numerical treatment of the bound, autoionizing continuum and continuum levels, and indicates how to find hitherto unknown low-lying stationary levels. An example, the splitting of the ground level, has been found numerically by an iterative shooting method.
03.65.Ge Solutions of wave equations: bound states
02.60.Lj Ordinary and partial differential equations; boundary value problems
35Q40 Equations from quantum mechanics
Issue 11 (18 March 2005)
Received 1 November 2004
Published 2 March 2005
S Barcza 2005 J. Phys. A: Math. Gen. 38 2469
Piotr Nowakowski and Marek Napiórkowski 2009 J. Phys. A: Math. Theor. 42 475005
Gloria M Spirou et al 2005 Phys. Med. Biol. 50 N141
Thomas R. Ayres et al. 1998 ApJ 496 428
H Pursch et al 2002 J. Phys. D: Appl. Phys. 35 1757
B N J Persson 2009 J. Phys.: Condens. Matter 21 485001
Ximin Liu 2001 J. Phys. A: Math. Gen. 34 5463
A. B. Verchovsky et al. 2004 ApJ 607 611
Xiaosheng Wu et al 2009 J. Micromech. Microeng. 19 125008
Ross I Berbeco et al 2005 Phys. Med. Biol. 50 4481