On the Growth Properties of Solutions for a Generalized BiAxially Symmetric Schr\"{o}dinger Equation 
Received:October 30, 2015 Revised:June 08, 2016 
Key Word:
Schro\"{o}dinger equation scattering potential Jacobi polynomials order and type

Fund ProjectL: 
Author Name  Affiliation  Devendra KUMAR  Department of Mathematics, Faculty of Sciences AlBaha University, P.O.Box1988, Alaqiq, AlBaha65431, Saudi Arabia, K.S.A.  Payal BISHNOI  Department of Mathematics, M.M.H. College, Ghaziabad (U.P.), India  Mohammed HARFAOUI  University Hassan IICasablanca, Laboratory of Mathematics, Cryptography and Mechanics, F.S.T, B.O.Box 146, Mohammedia, Morocco 

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Abstract: 
In this paper, we have considered the generalized biaxially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2V(r)\} \varphi=0,$$ where $\mu,\nu\ge 0$, and $rV(r)$ is an entire function of $r=+(x^2+y^2)^{1/2}$ corresponding to a scattering potential $V(r)$. Growth parameters of entire function solutions in terms of their expansion coefficients, which are analogous to the formulas for order and type occurring in classical function theory, have been obtained. Our results are applicable for the scattering of particles in quantum mechanics. 
Citation: 
DOI:10.3770/j.issn:20952651.2017.02.010 
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