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Symbolic Math Approach To Solve Particle-in-the-Box and H-Atom Problems

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Abstract

The Schrödinger equation can be solved exactly for the hydrogen atom. In this assignment, students will solve the equation symbolically using Mathcad's derivatives feature. The result is an expression for the energy levels of the hydrogen atom. Students will also prove that the radial part of the wave function is normalized and explore the concept of an orbital. This exercise is intended for junior-level students who have been introduced to quantum mechanics. Students should be able to solve the particle-in-the-box problem and plot the wave functions for the first several energy levels and have some experience with derivatives and integrals in Mathcad.

Figure 1. Probability density for radial part of the hydrogen 1s wave function.

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Version	Student	Instructor
Mathcad 12	H_AtomStudent.mcd	H_AtomInstructor.mcd

Version	Student	Instructor
Mathcad 12	H_AtomStudent.pdf	H_AtomInstructor.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Element: Hydrogen;

Pedagogy: Computer-Based Learning;

Topics: Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation