(1) Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700 032, India;(2) Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur, 721 302, India
Abstract:
We find the energy levels of a free particle confined in a two
dimensional infinite potential well having super-circular boundary
(|x|n+|y|n=an where n is a rational number and a is a
positive real number) by perturbing about the equivalent circle
(n=2). The ground state energies are very accurate over a wide
range of n and can be improved further by introducing a
phenomenological constant
determined from the knowledge of exact
results available for diamond (n=1). For excited states, we find
that the shape effect can cause parametric resonance which can lead
to singlet-triplet crossing.