Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Antoni BensenyAtomic orbitals and their representation are well known among the scientific comunity, and yet they hide certain complications that have not been taken into account properly. This work pretends to define atomic orbitals as electronic equidensity surfaces and to computate an interactive visualitzation which should show the different shapes of each orbital by using proper sections. It will be necessary to obtain and make a detailed analysis of the hydrogen atom eigenfunctions for each principal quantic number triplet n, l and m. Density functions and their derivatives will have to be calculated with Legendre and Laguerre associated polynomials recurrence formulas. A different study of the characteristics of all the parts of equation will provide information about the orbital critical points, which will be the basis of the visual computational method to minimize the calculations and obtain an efficient and fast programming result.