About the disposition of energy levels

作者：Liverts Evgeny Z^*; Dinur Nir Nevo

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(47): 475301.

DOI：10.1088/1751-8113/45/47/475301

The unique properties of central potential of the form -beta e(-r) r(gamma) were studied using the recently developed critical parameter technique. The particular cases of gamma = 0 and gamma = -1 yield, respectively, the exponential and Yukawa potentials widely used in atomic, molecular and nuclear physics. We found different behavior of the energy levels of this potential for three different ranges of the value of gamma. For gamma >= 0 it was found that the energy of bound states with the same principal quantum number N decreases with increasing angular momentum l. The Gaussian and Woods-Saxon potentials also show this behavior. In contrast, for -2 < gamma <= -1 increasing l gives a higher energy, resembling the Hulthen potential. However, a potential with -1 < gamma < 0 possesses mixed properties, which give rise to several interesting results. For one, the order of energy levels with different quantum numbers is not preserved when varying the parameter beta. This leads to a quantum degeneracy of the states, and in fact, for a given value of gamma we can find the values beta(thr) for which two energy levels with different quantum numbers coincide. Another interesting phenomenon is the possibility, for some values of gamma in this range, for two new energy levels with different quantum numbers to appear simultaneously when beta reaches their common critical value.

• 出版日期2012-11-30