The Particle in a Box Warrants an Examination

• URL: http://arxiv.org/abs/2204.07577v3
• Date: Sat, 4 Jun 2022 13:41:44 GMT
• Title: The Particle in a Box Warrants an Examination
• Authors: John R. Klauder
• Abstract summary: Using canonical quantization, this example has been fully studied thanks to its simplicity. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that nesaeccsrily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.

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