Double Potential Well

Hasan Hüseyin Erbil, Ahmet Saim Selvi

In some molecules such as ammonia, double vibrations are observed at small energies. These small vibrations are thought to arise from double well potentials. To explain these small energy gaps, double potential wells are investigated, and complex calculations are made. Until recently, since the exact solution of the Schrödinger equation was not known, approximate solutions were always obtained. The exact solution of the Schrödinger equation is now known. In previous studies, a simple procedure for the general solution of the radial Schrödinger Equation has been found for spherical symmetric potentials without making any approximation. In this article, the Schrodinger equation was solved with this new solution method. It has been applied to the oscillations through a barrier tunneling potential for a particle in a central quadratic deformed potential well (double potential well). It is seen that there is no need to look for complex potentials to explain the double wells observed in small vibrations in ammonia and similar molecules, they were compared with experimentally measured energies. The results were found to be fully compatible. It has been seen that there can always be double well potentials at small energies for all molecules, atomic nuclei, and similar particles with angular momentum other than zero.

H. Bartel Williams

Haijun Chen

Double-well potentials are important potential models that underlie the study of macroscopic quantum tunneling in Bose–Einstein Condensates (BECs), which are most commonly constructed in the form of a combination of a finite square-well potential and a square potential barrier. We propose another possibility of constructing a double-well potential, which consists of the combination of a square-well potential and a movable Gaussian-type potential barrier, and by adjusting the width, height, symmetry, and position of the movable potential barrier, symmetric and asymmetric double-well potentials with rich structures can be constructed. By numerically solving the Gross–Pitaevskii equation, we give the ground state structures of the BEC in this double-well potential, and then study the tunneling dynamics in this double-well potential. Different from trivial symmetric barrier displacement, the independently tunable two half-Gaussian widths bring an extra control degree of freedom; it is shown that the ground–state properties and tunneling dynamics are far more sensitive to asymmetric segmented barriers than to symmetrically shifted barriers. This feature offers a flexible strategy for atomic manipulation and is not merely a trivial qualitative observation.

Jin-Hui Li, Zhi-Jian Li

We first present an analytical solution of the single and double solitions of Bose—Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations (position and time) between two dark solitons can be controlled by its depth.