Kousar Shaheen et al., International Journal of Advanced Trends in Computer Science and Engineering, 10(3), May - June 2021, 2513 – 2523 2513 Python program to generate spherical harmonic Kousar Shaheen 1 , Roohi Zafar 1 , Saba Javaid 1 1 Department of Physics, NED University of Engineering and Technology, Pakistan kousarshaheen416@gmail.com roohizj@neduet.edu.pk hars4@yahoo.com , ABSTRACT A generalized Python program has been developed to show pictorial form of wave function of hydrogen and hydrogen like atoms. This program will be helpful to teach solution of Schrodinger equation for hydrogen and hydrogen like atoms to undergraduate students. The python program not only shows pictorial form of the wave function but it also gives analytical form of the wave function. The wave- functions and the orbital from 1s (1,0,0) to 9f (9,3,0) are presented in this article. Key words: Probability Distribution Function, Associated Laguerre Polynomials, Associated Legendre Polynomials, Hyper geometric function. 1. INTRODUCTION Hydrogen atom is of fundamental important, as it is the only atom for which Schrödinger’s equation can be solved exactly and the wave function of this atom provides the basis for many approximate methods to solve many electron atoms. It has been found that students, which are studied in introduction of Quantum Physics, misinterpret polar graphs and hydrogen eigen state probability distribution plots. In 2002, Budde et.al investigated that according to their research, experience, gaining knowledge of quantum atomic model increases many problems. Detailed survey of various college students’ preconceptions problems may be found [1,2]. In 2002, Müller et.al found that many college students believe that in atom just like the Bohr’s model, electrons orbiting around the nucleus. Although a number of them recognize that it’s not correct, this idea appears to be very resistant [3]. There are new approaches to solve these troubles and lead college students to better understanding [2-4]. In 1962, Fowles et.al generated a general equation of Cartesian coordinate with modification of Schrodinger’s equation by separable variable method and making assumption that a wave function depends upon four variables x, y, z, r [5]. The Mathematica software program offers a variety of tools for understanding, manipulate and visualize atomic and Molecular systems, in which, orthogonal polynomials and Clebsch- Gordan Coefficients, polar plots, spherical plots, density plots, Contour plots and animation are included [6-7]. In 2013, Chung et.al described that how Winplot software programs can be used to understand and visualize micorbitals and wave functions of a hydrogen like atom [8]. In this work, we transformed probability distribution function from Polar coordinate system to cartesian coordinate system by modifying spherical harmonics and radial distribution function. [9-11] 2.THEORY Schrodinger equation for hydrogen and hydrogen like atom is a fundamental equation in quantum mechanics to solve wave functions for these atoms, which describes the state of the system. The wave equation for one electron system in the field of a nucleus of charge Ze is given by equation ܪ = ቆ− ћ ଶ 2 ∇ ଶ − ଶ ݎቇ = ܧ 1 Where E is the total energy of the system, is the total wavefunction and Z is the atomic number. Since coulomb potential energy and the boundary conditions are spherically symmetric,solutions to Schrödinger's equation may be solved by using separation of variable method and the wavefunction can be written as the product of a radial and an angular part ( ݎ, ߠ, ) = 1 ݎ( , ݎ) ( ߠ, ) 2 Where ( ߠ, ) a spherical harmonics with l is orbital quantum number, an integer with values≥ 0. ISSN 2278-3091 Volume 10, No.3, May - June 2021 International Journal of Advanced Trends in Computer Science and Engineering Available Online at http://www.warse.org/IJATCSE/static/pdf/file/ijatcse1421032021.pdf https://doi.org/10.30534/ijatcse/2021/1431032021