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
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.
PACS: 03.65.-W – Quantum mechanics / 31.15.Md – Perturbation theory / 03.65.Ge – Solutions of wave equations: bound states
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007