Wolfgang Pauli

Die allgemeinen Prinzipien der Wellenmechanik

Unbestimmtheitsprinzip und Komplementaritat 2. Die letzte entscheidende Wendung der Quantentheorie ist erfolgt durch De Broglies Entdeckung der Materiewellen 3, Heisenbergs Auffindung der Matrizenmechanik 4 und Schrodingers 5 allgemeine wellenmechanische Differentialgleichung, welche die Verbindung zwischen diesen beiden Ideenkreisen herzustellen ermoglichte. Durch Heisenbergs Unbestimmtheitsprinzip 6: und die an dieses anschliesenden prinzipiellen Erorterungen Bohrs 7 kamen dann die Grundlagen der Theorie zu einem vorlaufigen Abschlus.

Zur Quantendynamik der Wellenfelder

Einleitung. — I. Allgemeine Methode. § 1. Lagrangesche und Hamiltonsche Form von Feldgleichungen, Energie und Impulsintegrale. § 2. Kanonische Ver-tauschungsrelationen (V.-R.) fur stetige Raum—Zeit-Funktionen. Energie und Impulssatz in der Quantendynamik. § 3. Relativistische Invarianz der V.-R. bei invarianter Lagrangefunktion. — II. Aufstellung der Grundgleichungen der Theorie fur elektromagnetische Felder und Materiewellen. § 4. Schwierigkeiten der Quantelung der Max wellschen Gleichungen, Notwendigkeit von Zusatzgliedern. § 5. Uber das Verhaltnis der hier aufgestellten Gleichungen zu fruheren Ansatzen fur die Quantenelektrodynamik ladungsfreier Felder. § 6. Differential- und Integralform der Erhaltungssatze von Energie und Impuls fur das gesamte Wellenfeld. — III. Annaherungsmethoden zur Integration der Gleichungen und physikalische Anwendungen.

Zur Quantenmechanik des magnetischen Elektrons

Es wird gezeigt, wie man zu einer Formulierung der Quantenmechanik des magnetischen Elektrons nach der Sehrodinger sehen Methode der Eigen funktion en ohne Verwendung zweideutiger Funktionen gelangen kann, indem man, gestutzt auf die allgemeine Dirac-Jordansche Transformationstheorie, neben den Ortskoordinaten jedes Elektrons, um seinen rotatorischen Freiheitsgraden Rechnung zu tragen, die Komponente seines Eigenimpulsmomentes in einer festen Richtung als weitere unabhangige Veranderliche einfuhrt. Im Gegensatz zur klassischen Mechanik kann diese Variable jedoch, ganz unabhangig von irgend einer speziellen Art der auseren Kraftfelder, nur die Werte (Math) und (Math) annehmen. Das Hinzutreten der genannten neuen Variable bewirkt daher bei einem Elektron einfach ein Aufspalten der Eigenfunktion in zwei Ortsfunktionen ψα, ψβ und allgemeiner bei N Elektronen in 2N Funktionen, die als die „Wahrscheinlichkeitsamplituden” dafur zu betrachten sind, das in einem bestimmten stationaren Zustand des Systems nicht nur die Lagenkoordinaten der Elektronen in vorgegebenen infinitesimalen Intervallen liegen, sondern auch die Komponenten ihrer Eigenmomente in der festgewahlten Richtung bei (Math) vorgegebene Werte haben* Pauli (1927b)

Zur Quantentheorie der Wellenfelder II

Fur die Quantentheorie der Wellenfelder wird der Zerfall des Gesamttermsystems in nichtkombinierende Teilsysteme untersucht. Aus den Invarianzeigenschaften der Hamiltonschen Funktion werden hierbei die Integrale der Bewegungsgleichungen hergeleitet; ferner ergibt sich durch Betrachtung der Eichinvarianz eine befriedigende Formulierung der Elektrodynamik ohne Zusatzglieder. Der mathematische Zusammenhang zwischen Wellentheorie und Partikeltheorie wird diskutiert.

Einige die Quantenmechanik betreffende Erkundigungsfragen

ZusammenfassungEinige Fragen und Bemerkungen betreffs: A. Die imaginäre Einheit in der Schrödingergleichung und der Transformationstheorie: — B. Die mangelnde Analogie zwischen Photon und Elektron. — C. Das Zugänglichermachen der Spinorreohnung.

Phenomenon and Physical Reality

In the following lecture I wish to give some indications as to which problems, connected with the key-words phenomenon and reality, play an important part in contemporary physics, without claiming anything like mastery over this inexhaustible theme. In the course of my remarks I shall also touch on controversial questions, for it is towards them that general interest is chiefly directed. To give the philosophers their bearings, I may say at once that I am not myself an adherent of any particular philosophical trend with a name ending in “-ism”. I am moreover opposed to associating particular “-isms”with particular physical theories, such as for instance the theory of relativity or quantum or wave mechanics, although this is occasionally done by physicists. My general tendency is rather to hold a middle course between extreme directions. In this sense I think it best to consider first of all how phenomenon and reality occur in the physicist’s everyday professional life.

Space, Time and Causality in Modern Physics

In many respects the present appears as a time of insecurity of the fundamentals, of shaky foundations. Even the development of the exact sciences has not entirely escaped this mood of insecurity, as appears, for instance, in the phrases “crisis in the foundations” in mathematics, or “revolution in our picture of the universe” in physics. Indeed many concepts apparently derived directly from intuitive forms borrowed from sense-perceptions, formerly taken as matters of course or trivial or directly obvious, appear to the modern physicist to be of limited applicability. The modern physicist regards with scepticism philosophical systems which, while imagining that they have definitively recognised the a priori conditions of human understanding itself, have in fact succeeded only in setting up the a priori conditions of the systems of mathematics and the exact sciences of a particular epoch.

Einstein’s Contribution to Quantum Theory

If new features of the phenomena of nature are discovered that are incompatible with the system of theories assumed at that time, the question arises, which of the known principles used in the description of nature are general enough to comprehend the new situation and which have to be modified or abandoned. The attitude of different physicists on problems of this kind, which makes strong demands on the intuition and tact of a scientist, depends to a large extent on the personal temperament of the investigator. In the case of Planck’s discovery in 1900 of the quantum of action during the course of his famous investigations of the law of the black-body radiation, it was clear that the law of the conservation of energy and momentum and Boltzmann’s principle connecting entropy and probability, were two pillars sufficiently strong to stand unshaken by the development resulting from the new discovery. It was indeed the faithfulness to these principles which enabled Planck to introduce the new constant h, the quantum of action, into his statistical theory of the thermodynamic equilibrium of radiation.

Die Verletzung von Spiegelungs-Symmetrien in den Gesetzen der Atomphysik

The reflections of charge (C), space-coordinates (P) and time (T) and, particularly in connection with the space reflection, the distinction between polar vector and axial vector, scalar and pseudoscalar products are explained. The three different kinds of strong, medium (electromagnetic) and weak interactions are introduced. While the first two of them fulfil all reflection invariances mentioned separately,Lee andYang showed (1956) that for the weak interactions no sufficient empirical evidence existed for the reflection invariances, and they also suggested experiments for checking them. The qualitative aspect of the experimental results available in November 1957, which show the violation of theC- and theP-invariance for weak interactions, is reviewed. The methods hereby applied are betadecay of oriented nuclei, polarisation of emitted electrons in beta-decay, beta-gamma-correlation, asymmetry in the decay of μ-mesons generated by π-meson-decay. The solution of the Θ-τ-puzzle by the assumption of a single particle (K-meson) without defined parity is mentioned. In the concluding section, some aspects of the unsolved theoretical problems of the deeper reasons for the symmetry violations of the weak interactions are briefly discussed which will possibly also lead into open cosmological questions.

On the Earlier and More Recent History of the Neutrino

The continuous energy spectrum of beta rays, discovered by J. Chadwick in 1914,’ immediately raised difficult problems of theoretical interpretation. Was it to be ascribed directly to the primary electrons emitted by the radioactive nucleus, or to secondary processes? The first view, which turned out to be the correct one, was advocated by C. D. Ellis,2 the second by L. Meitner.3 The latter appealed to the fact, known from alpha and gamma rays, that nuclei possess discrete energy levels. She focused the discussion on the discrete energies of the electrons which are likewise observed in many beta-radioactive nuclei. Ellis was able to interpret these as electrons ejected from the outer shells by monochromatic nuclear gamma rays by internal conversion, and to relate them to the observed X-ray lines. According to L. Meitner’s theory however, at least one of the electrons of discrete energy was a genuine primary electron from the nucleus, which could then likewise eject other secondary electrons of lower energies from the outer shells.4 This postulated primary electron of discrete energy could however never be detected. Moreover there are beta-radioactive nuclei, such as RaE, which do not emit gamma rays and in which moreover the electrons of discrete energy are completely absent.