Physics – Quantum Physics
Scientific paper
2011-07-30
Physics
Quantum Physics
18 pages, 9 figures
Scientific paper
Quantum mechanics in one dimension, with potentials unbounded below, is studied using the asymptotic iteration method. After a brief introduction and a summary of known results, we focus on the cosh-sech potential, for which, we numerically obtain the eigen-spectrum and its variation with respect to the potential parameters. Thereafter, we look at the parametric variation of the transition wavelength between a bound state lying inside the valley of the potential and another appearing above the potential maximum. The purpose of this exercise is to suggest an experimentally viable method of confirming the existence of such unusual, above--maximum bound states. Finally, we construct a modified potential which is bounded or unbounded below, depending on the value of a parameter in the potential. We show how the spacing between certain energy levels gradually decrease as we tune the parameter to approach the value for which unboundedness arises. The link between degeneracy and unboundedness is thus established in a limiting sense. Overall, despite existing lore that unbounded potentials are unphysical, we are able to show through our work, that there are interesting consequences and questions which seem to motivate further investigations.
Dutt Avik
Kar Sayan
Nath Trisha
Parwani Rajesh
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