Eur. Phys. J. D 46, 41-50 (2008)
https://doi.org/10.1140/epjd/e2007-00282-6

Energy levels of a particle confined in a super-circular box

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

Corresponding author: ^a tpjkb@iacs.res.in

Received: 22 May 2007
Revised: 13 August 2007
Published online: 5 October 2007

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.