Abstract:
A two-dimensional hydrogen atom is analyzed in elliptic
coordinates. Separation of the variables reduces the problem to
the solution of the Ince equation in the complex plane subject to
certain boundary conditions. It is shown that in the limits
$R\rightarrow 0$ and $R\rightarrow\infty$ ($R$ is a parameter that
specifies the elliptic coordinates) the obtained solutions go over
to polar and parabolic bases, respectively. The explicit form of
the elliptic basis is given for the lowest quantum states.
Citation:
L. G. Mardoyan, G. S. Pogosyan, A. N. Sisakyan, V. M. Ter-Antonyan, “Two-dimensional hydrogen atom. I. Elliptic basis”, TMF, 61:1 (1984), 99–117; Theoret. and Math. Phys., 61:1 (1984), 1021–1034