Analytical Solutions to the $D$-Dimensional Schr?dinger Equation with the Eckart Potential
Jie Gao, Min-Cang Zhang**
College of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119
Abstract ：The analytical solutions to the Schr?dinger equation with the Eckart potential in arbitrary dimension $D$ is investigated by using the Nikiforov–Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunction is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for $D$=3, and the resulting energy equation agrees well with that obtained by other methods.
收稿日期: 2015-11-05
出版日期: 2016-01-29
:
03.65.-w
(Quantum mechanics)
03.65.Ge
(Solutions of wave equations: bound states)
03.65.Db
(Functional analytical methods)
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2016, Vol. 33 
