Effect of the Electric and Magnetic Fields with Aharonov–Bohm Flux Field in Quantum Dots

Abstract

This paper has solved the nonrelativistic equation with the external uniform electric potential and magnetic and Aharonov–Bohm (AB) fields in a dot. We have obtained the three-term recurrence relation for the expansion coefficients using the series method. In continuing, we have found two different conditions. Then, using the obtained conditions, we have calculated the energy eigenvalues and eigenfunction. We have then obtained the main thermodynamic quantities such as the free energy, mean energy, entropy, specific heat, magnetization and persistent currents for our system. Also, we extended the calculations to an interaction-free [Formula: see text]-body system. The obtained analytic results are compared with other results, and some of the obtained results are discussed, too.

Caloric Effect Due to the Aharonov–Bohm Flux in an Antidot

“…This effect was tested experimentally by interference by Chambers in 1960 (among other groups at the same time) [72]. Although these potentials are not directly measurable, their impact on physical phenomena has been intensely studied in areas such as electronic transport [73][74][75] and thermodynamics [76,77].…”

Nonrelativistic solutions of Schrödinger equation and thermodynamic properties with the proposed modified Mobius square plus Eckart potential

“…However, exact solutions of the Schrödinger equation are limited to some cases [10] , [11] , [12] . Researchers have attempted to solve the Schrödinger and other wave equations using mathematical methods such as Laplace transform method [13] , [14] , [15] , path integral method [16] , algebraic method [17] , shifted 1/N expansion [18] , Nikiforov–Uvarov (NU) Method [19] , [20] , [21] , [22] , [23] , [24] , [25] , formula method [26] and many others [27] , [28] , [29] , [30] . In the present paper, we shall focus our attention on the proposed modified Mobius square plus Eckart (MMSPE) potential.…”