E. P. Wigner

On Unitary Representations of the Inhomogeneous Lorentz Group

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.

Distribution functions in physics: Fundamentals

This is the first part of what will be a two-part review of distribution functions in physics. Here we deal with fundamentals and the second part will deal with applications. We discuss in detail the properties of the distribution function defined earlier by one of us (EPW) and we derive some new results. Next, we treat various other distribution functions. Among the latter we emphasize the so-called P distribution, as well as the generalized P distribution, because of their importance in quantum optics.

Calculation of the natural brightness of spectral lines on the basis of Dirac's theory

ZusammenfassungEs werden die Diracschen Gleichungen der Wechselwirkung zwischen Atom und Strahlung in einer von der üblichen verschiedenen Art näherungsweise gelöst. Die Lösungen gelten während der ganzen Zeit, die für die Emission praktisch in Betracht kommt, mit der gleichen Näherung und liefern den Intensitätsverlauf in den Emissionslinien des Atoms.

On an Algebraic generalization of the quantum mechanical formalism

One of us has shown that the statistical properties of the measurements of a quantum mechanical system assume their simplest form when expressed in terms of a certain hypercomplex algebra which is commutative but not associative.1 This algebra differs from the non-commutative but associative matrix algebra usually considered in that one is concerned with the commutative expression ½(A × B + B × A) instead of the associative product A × B of two matrices. It was conjectured that the laws of this commutative algebra would form a suitable starting point for a generalization of the present quantum mechanical theory. The need of such a generalization arises from the (probably) fundamental difficulties resulting when one attempts to apply quantum mechanics to questions in relativistic and nuclear phenomena.

About the Pauli exclusion principle

Die Arbeit enthalt eine Fortsetzung der kurzlich von einem der Verfasser vorgelegten Note „Zur Quantenmechanik der Gasentartung“, deren Ergebnisse hier wesentlich erweitert werden. Es handelt sich darZusammenfassungDie Arbeit enthält eine Fortsetzung der kürzlich von einem der Verfasser vorgelegten Note „Zur Quantenmechanik der Gasentartung“, deren Ergebnisse hier wesentlich erweitert werden. Es handelt sich darum, ein ideales oder nichtideales, dem Paulischen Äquivalenzverbot unterworfenes Gas zu beschreiben mit Begriffen, die keinen Bezug nehmen auf den abstrakten Koordinatenraum der Atomgesamtheit des Gases, sondern nur den gewöhnlichen dreidimensionalen Raum benutzen. Das wird ermöglicht durch die Darstellung des Gases vermittelst eines gequantelten dreidimensionalen Wellenfeldes, wobei die besonderen nichtkommutativen Multiplikationseigenschaften der Wellenamplitude gleichzeitig für die Existenz korpus-kularer Gasatome und für die Gültigkeit des Paulischen Äquivalenzverbots verantwortlich sind. Die Einzelheiten der Theorie besitzen enge Analogien zu der entsprechenden Theorie für Einsteinsche ideale oder nichtideale Gase, wie sie von Dirac, Klein und Jordan ausgeführt wurde.

On the Possibility of a Metallic Modification of Hydrogen

Any lattice in which the hydrogen atoms would be translationally identical (Bravais lattice) would have metallic properties. In the present paper the energy of a body‐centered lattice of hydrogen is calculated as a function of the lattice constant. This energy is shown to assume its minimum value for a lattice constant which corresponds to a density many times higher than that of the ordinary, molecular lattice of solid hydrogen. This minimum—though negative—is much higher than that of the molecular form. The body‐centered modification of hydrogen cannot be obtained with the present pressures, nor can the other simple metallic lattices. The chances are better, perhaps, for intermediate, layer‐like lattices.

The Problem of Measurement

The standard theory of measurements in quantum mechanics is reviewed with special emphasis on the conceptual and epistemological implications. It is concluded that the standard theory remains the only one which is compatible with present quantum mechanics. Hence, if one wants to avoid the conclusion that quantum mechanics only gives probability connections between subsequent observations, the quantum-mechanical equations would have to be modified. Particular attention is paid to the case that the measuring apparatus is macroscopic and its state vector not accurately known before the measurement.

Calculation of the Rate of Elementary Association Reactions

An upper limit for the rate of association reactions is found by determining the probability of a decrease of ihe relative energy of two atoms below zero energy, under the influence of.a third body. The relation of this approximate calculation to the rigorous solution of the problem is discussed in Section 2. The results are applied to the recombination of J atoms, measured by Rabinowitch and Wood. Numerically, the agreement is quite good; however, the calculated values are somewhat too low, which cannot be explained by an inaccuracy of the method. Reasons for the discrepancy other than the possible nonadiabatic character of the reaction are discussed.

Effects of the electron interaction on the energy levels of electrons in metals

The very simplest form of the theory of the energy bands in metals 1 gave for many problems such accurate explanations of often very intricate properties of metals and alloys that it may well appear superfluous to consider extensions of the simple form of the theory. Nevertheless I believe that if the theory of metals is to broaden so as to include an even greater variety of phenomena, however satisfying the simple picture is for some purposes, the development of a more rigorous theory would not be superfluous.

Remarks on the Mind-Body Question

F. Dyson, in a very thoughtful article,1 points to the everbroadening scope of scientific inquiry. Whether or not the relation of mind to body will enter the realm of scientific inquiry in the near future-and the present writer is prepared to admit that this is an open question-it seems worthwhile to summarize the views to which a dispassionate contemplation of the most obvious facts leads. The present writer has no other qualification to offer his views than has any other physicist and he believes that most of his colleagues would present similar opinions on the subject, if pressed.