On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined

Details On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined

2001-01-27

arxiv.org/abs/math-ph/0101030v2

Czech. J. Phys. 52, 351 ( 2002 )

Physics

Mathematical Physics

10 pages, no figures, Latex file, To appear in the Czech. J. Phys

Scientific paper

10.1023/A:1015425301283

The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi - exact solutions for the ground and first excited states are also given for the above potential confined to an impenetrable cylindrical (D=2) or spherical (D=3) wall.

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