Author(s)

John R. Klauder

Department of Physics and Department of Mathematics, University of Florida, Gainesville, USA.

The particle in a box is a simple model that has a classical Hamiltonian H = p² (using 2m = 1), with a limited coordinate space, -b < q < b, where 0 < b < ∞. 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 necessarily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.

Particle, Affine Quantization, Canonical Quantization (CQ)

Klauder, J. (2022) The Particle in a Box Warrants an Examination. Journal of High Energy Physics, Gravitation and Cosmology, 8, 623-627. doi: 10.4236/jhepgc.2022.83043.