Volume 112, Number 1, October 2015
|Number of page(s)||5|
|Published online||26 October 2015|
Exact solution of the Schrödinger equation for the inverse square root potential
Institute for Physical Research, NAS of Armenia - 0203 Ashtarak, Armenia
Received: 28 August 2015
Accepted: 5 October 2015
We present the exact solution of the stationary Schrödinger equation for the potential . Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with non-constant coefficients of two confluent hypergeometric functions of a shifted argument. Alternatively, the solution is written through the first derivative of a tri-confluent Heun function. Apart from the quasi-polynomial solutions provided by the energy specification , we discuss the bound-state wave functions vanishing both at infinity and in the origin. The exact spectrum equation involves two Hermite functions of non-integer order which are not polynomials. An accurate approximation for the spectrum providing a relative error less than 10−3 is . Each of the wave functions of bound states in general involves a combination with non-constant coefficients of two confluent hypergeometric and two non-integer order Hermite functions of a scaled and shifted coordinate.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 02.30.Ik – Integrable systems / 02.30.Gp – Special functions
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.