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