Comments on Good's Proposal for New Rules of Quantization

TL;DR

This paper critically examines Good's proposed rules of quantization, highlighting their limitations and incompatibility with standard quantum theory, especially regarding energy spectra and field models, despite some derivations of mass spectra.

Contribution

The paper provides a detailed analysis of Good's quantization proposal, demonstrating its shortcomings and contrasting it with standard quantum theory, including derivations of the Klein-Gordon mass spectrum.

Findings

Fails to produce correct hydrogen atom energy spectrum

Cannot recover standard quantum theory for field models

Derives a Klein-Gordon mass spectrum with negative masses

Abstract

In a recent paper \cite{[Good1]} Good postulated new rules of quantization, one of the major features of which is that the quantum evolution of the wave function is always given by ordinary differential equations. In this paper we analyse the proposal in some detail and discuss its viability and its relationship with the standard quantum theory. As a byproduct, a simple derivation of the `mass spectrum' for the Klein-Gordon field is presented, but it is also shown that there is a complete additional spectrum of negative `masses'. Finally, two major reasons are presented against the viability of this alternative proposal: a) It does not lead to the correct energy spectrum for the hydrogen atom. b) For field models, the standard quantum theory cannot be recovered from this alternative description.