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American Journal of Physics

On the principles of quantum mechanics and the reduction of the wave packet

Roger Balian

Published Nov 1, 1989• 22 citations
Publisher

Abstract

The principles of quantum mechanics are reviewed in a form where the concept of state appears both more transparent and more general than in current textbooks. The so-called reduction of the wave packet is then derived from some of these principles (such as the compatibility of commuting observables and the fact that a variance cannot be negative), instead of being posed as a separate postulate.

DOI
10.1119/1.15813

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The principles of quantum mechanics are reviewed in a form where the concept of state appears both more transparent and more general than in current textbooks. The so-called reduction of the wave packet is then derived from some of these principles (such as the compatibility of commuting observables and the fact that a variance cannot be negative), instead of being posed as a separate postulate.
The theory of measurement is reasonably interpreted without any abrupt and noncausal change of a state, namely, with no “reduction of a wave packet”, in the framework of quantum mechanics. Though a process of measurement is causal in the usual quantum-mechanical sense, it is possible to utilize the concept of the “reduction of a wave packet” without any loss of compatibility. The Stern-Gerlach experiment is put to a careful study to show that the present interpretation is consistent with experiment.
The one-particle Schrödinger and Dirac equations are derived, without making any quantization hypothesis, from the postulate that an elementary particle is a physical wave packet of dynamically varying form and size, rather than a pointlike object located somewhere within the support of a wavefunction that serves only as a mathematical probability amplitude. An isolated multiparticle system can, similarly, be described in principle as a set of interacting wave packets governed by coupled one-particle equations, a picture from which, in the nonrelativistic limit, the multiparticle Schrödinger equation can be obtained as a sufficiency condition for the system to have a conserved total energy equal to a particular value E .
The uncertainty principle, formulated by Heisenberg in 1927, is a fundamental principle in quantum mechanics. It forces us to review key concepts of classical physics, and from this analysis are born the concepts of quantum physics. Consequences of the Uncertainty principle also introduces the concept of incompatible sizes, a completely new concept compared to classical physics. A state of the system, which we call a quantum state, will be determined from the knowledge of a set maximum of certain quantities that are independent and compatible with each other. A measurable physical quantity is called an observable. If at a given moment a measurement is performed by one or more compatible observables it is said they are performing an observation of the system. The basic principles of quantum mechanics are expressed by a number of postulates. Their numbers and can vary from one text to another.