Devendra KUMAR,Payal BISHNOI,Mohammed HARFAOUI.On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation[J].数学研究及应用,2017,37(2):214~222
On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation
On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation

DOI：10.3770/j.issn:2095-2651.2017.02.010

 作者 单位 Devendra KUMAR Department of Mathematics, Faculty of Sciences Al-Baha University, P.O.Box-1988, Alaqiq, Al-Baha-65431, Saudi Arabia, K.S.A. Payal BISHNOI Department of Mathematics, M.M.H. College, Ghaziabad (U.P.), India Mohammed HARFAOUI University Hassan II-Casablanca, Laboratory of Mathematics, Cryptography and Mechanics, F.S.T, B.O.Box 146, Mohammedia, Morocco

In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ 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.

In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ 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.