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Construction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogen-like Systems

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Abstract

This Mathcad document allows users to explore the characteristics of the components of the radial electronic wave function of the hydrogen atom, R(r) (where r is the distance of the electron from the nucleus). Within this exercise, R(r) is separated into four parts: a normalization constant, a polynomial function of r, an associated Laguerre polynomial of r, and an exponential function of r. After choosing quantum numbers n and l, users can evaluate and graphically display the component functions of R(r) separately. After combining these components, the entire wave function is constructed and graphs of R(r) and its associated probability density are displayed. How each separate function of r affects the overall radial wave function can be investigated. Finally, users have an opportunity to discover some relationships between values of n, l, and certain properties of the radial electronic wave function and its associated probability density (such as the number of nodes and the most probable distance from the nucleus).

Figure 1. The First 5 Laguerre Polynomials

Downloads

Version	Download
Mathcad 12 XML	H_like_RadialFunctions.xmcd
Mathcad 11	H_like_RadialFunctions11.mcd

Version	Download
Mathcad 11	H_like_RadialFunctions.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation