A New View on the Uncertainty Principle

David Appell

Miguel Lunetta

Taizo Iijima, Mamoru Iwaki

In natural observation theory, input waveforms are observed using natural observation transforms. Especially in the case of the neighboring type, the effect of the uncertainty principle as it applies to a natural observation transform was clarified by using the equivalent time constant. This paper aims to characterize natural observation transforms of normal type in waveform observation from the point of view of the uncertainty principle. Besides the equivalent time constant, the average degree index is introduced to represent the uncertainty principle. It describes a relation between the equivalent time constant and the variance in the observation degree. This paper gives a new insight into the set of fundamental observed values of normal type from the point of view of observation resolution. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 45–54, 1998

P Marquardt, G. Galeczki

Clara Snow, Michael G. Messina

The Uncertainty Principle is usually discussed twice in a Quantum Chemistry course. The first discussion is a “pre-wave function” explanation that occurs before students know about wave functions, but do know the de Broglie hypothesis. The second description of the Uncertainty Principle is “post-wave function”, i.e., after students have learned about wave functions, operators, and expectation values. The more common pre-wave function explanations of the Uncertainty Principle can lead students to believe that the Uncertainty Principle sets limits upon what can be measured in the lab. This is the “measurement view” of the Uncertainty Principle. The Uncertainty Principle says something much deeper than this; particles do not possess some properties solely because of their wave nature. This is the “particle-centric view” of the Uncertainty Principle. We show that the Uncertainty Principle can be explained from the preferred particle-centric view when students only know about the de Broglie wavelength and basic statistics. To accompany this pre-wave function discussion of the Uncertainty Principle, we have designed an interactive Module that students can use to visualize the Uncertainty Principle from the particle viewpoint. We also describe a way to explain the Uncertainty Principle, which is complementary to the pre-wave function discussion, after the students know about wave functions, using the same elementary statistical analysis used in the pre-wave function presentation. We have designed a second interactive Module that students can use to visualize the Uncertainty Principle when particles are described by complex wave functions.

Peter Gibbins

It is shown that the uncertainty principle has nothing directly to do with the non-localisability of position and momentum for an individual system on the quantum logical view. The product Δx·Δp for localisation of the ranges of position and momentum of an individual system → ∞, while the quantities ΔX and ΔP in the uncertainty principle ΔX·ΔP ≥ ħ/2, must be given a statistical interpretation on the quantum logical view.