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Journal of Yuxi Normal University

The Explanatory Theory on the Energy Levels of an Object That is Bound in Gravitational Field

Luo Ling-xiao

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

On the basis of the explanatory theory of quantum phenomenon,the energy levels of a single pendulum,of a slide lump on a round smooth guide way in a vertical plane and of a slide lump in two butted smooth oblique planes are deduced.Because the explanatory theory of quantum phenomenon can reduce the difficulty of learning the quantum theory,it makes the idea of quantitatively teaching some quantum mechanics content in junior years of university or even in senior middle school more realistic.

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On the basis of the explanatory theory of quantum phenomenon,the energy levels of a single pendulum,of a slide lump on a round smooth guide way in a vertical plane and of a slide lump in two butted smooth oblique planes are deduced.Because the explanatory theory of quantum phenomenon can reduce the difficulty of learning the quantum theory,it makes the idea of quantitatively teaching some quantum mechanics content in junior years of university or even in senior middle school more realistic.
More than 35 years ago, French and Taylor1 outlined an approach to teach students and teachers alike how to understand “qualitative plots of bound-state wave functions.” They described five fundamental statements based on the quantum-mechanical concepts of probability and energy (total and potential), which could be used to deduce the shape of energy eigenfunctions. Despite these important and easy-to-follow statements, this approach has not been universally adopted in the teaching of quantum mechanics.2 For example, recent studies have shown that students' conceptual understanding of quantum mechanics on all levels is surprisingly lacking3 and that misconceptions are universal,4 including that of the relationship between the potential energy function and the resulting energy eigenfunction shape. At the same time, the teaching of quantum mechanical concepts in introductory physics has become increasingly important given the modern technological applications that are based on quantum theory (e.g., PET scans and MRIs). However, most treatments of quantum theory on the introductory level are cursory at best, leaving students with the impression that quantum mechanics is little more than abstract mathematics (a belief that remains with students in their future courses).
A detailed quantum mechanical treatment of the motion of a plane pendulum is given. Exact solution of the Schrödinger equation shows that the energy eigenfunctions and eigenvalues go over to those of a plane rotator for vanishing acceleration due to gravity g and to those of a harmonic oscillator in the limit of infinitely massive bob. In view of this, perturbation calculations have been done using rotator and oscillator basis, and conditions for convergence of the perturbation series in both cases have been discussed.
Much has been written in recent years about the strange features associated with the quantum-mechanical description of nature at the atomic level. Physics teachers should help their students to see that many of these mysterious features are direct results of interpretive principles added to the basic theory of quantum mechanics, and that therefore they may or may not reflect the best possible understanding we can achieve of how nature works at that level. This paper discusses three such principles and their connection to well-known quantum mysteries. The practical significance of distinguishing between quantum mechanics itself and these principles is that it remains possible that other explanatory ideas may be found which lead to less mysterious consequences.