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Illustrating the Bohr Correspondence Principle

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Abstract

The goal of this document is to introduce the Bohr Correspondence Principle in an activity immediately following the traditional lecture on the solution of the Schrödinger equation for the particle-in-a-1D-box (PIB) problem. An incomplete three-part Mathcad document is provided to the students. In part 1, students relate nodal features of the wavefunction to the quantum number (n) and are graphically reminded of the mathematical basis of quantization. Part 2 focuses on the interpretation of the square of the wavefunction as probability density; students are led to the conclusion that Quantum Mechanics (QM) and Classical Mechanics (CM) agree at large n. Part 3 illustrates that QM can be interpreted to agree with CM in a case that is adequately described by Kinetic Molecular Theory, which is based on CM. Students verify that n for an average He molecule in a 1-dm box at 298K is, indeed, large. A completed version of the document is available for teachers.

Figure 1. Probability density function for quantum state n=1, dotted line; classical mechanics probability density function, solid line.

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Version	Student	Instructor
Mathcad 2001	BCPstudent2001.mcd	BCPfaculty2001.mcd
Mathcad 8	BCPstudent8.mcd	BCPfaculty8.mcd

Version	Student	Instructor
Mathcad 2001	BCPstudent2001.pdf	BCPfaculty2001.pdf

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Keywords

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation