Is there a quantization condition for the classical problem of charge and pole? |
| |
Authors: | H A Cohen |
| |
Institution: | 1. Quantum Mechanics Research Group, School of Physical Science, La Trobe University, 3083, Melbourne, Australia
|
| |
Abstract: | In elementary derivations of the quantization of azimuthal angular momentum the eigenfunction is determined to be exp(im φ), which is “oversensitive” to the rotation φ → φ+2π, unlessm is an integer. In a recent paper Kerner examined the classical system of charge and magnetic pole, and expressed Π, a vector constant of motion for the system, in terms of a physical angle ψ, to deduce a remarkable paradox. Kerner pointed out that Π(ψ) is “oversensitive” to ψ → ψ+2π unless a certain charge quantization condition is met. Our explicandum of this paradox highlights the distinction between coordinates in classical and quantum physics. It is shown why the single-valuedness requirement on Π(ψ) is devoid of physical significance. We are finally led to examine the classical analog of the quantum mechanical argument that demonstrates the quantization of magnetic charge, to show that there is “no hope” of a classical quantization condition. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|