A. Rubinowicz: Quantum Mechanics

Albert Messiah

GREGORY A. BREIT

Theory of the Brownian motion of a Planck radiator in black body radiation.---In the case of a classical resonator it is shown that the motion takes place even though the emission and absorption is not unidirectional provided the radiation is not strictly monochromatic. This theory is then extended to the case of a quantized atom. Interference between the waves emitted by the atom and the surrounding radiation provides for the recoil actions without the assumption of unidirectional quanta. Statistically these have the same effect as Einstein's unidirectional quanta. This theory removes the contradiction postulated by Einstein between the Rubinowicz-Sommerfeld considerations and the requirements of classical Brownian motion. It leaves the wave-theory of light intact and is in agreement with Bohr's principle of correspondence.

Alfred Kastler

D URING MY FIRST YEAR as a student at the Ecole Normale Supérieure in Paris, our professor, Eugene Bloch, introduced us to quantum physics, which was seldom taught in France at that time. Like him, I was from Alsace and spoke German. He strongly advised me to read Arnold Sommerfeld's excellent book Atombau und Spektrallinien. When reading this book, I was particularly interested in the application of the principle of conservation of angular momentum in interactions between electromagnetic radiation and matter—an application that guided A. Rubinowicz to the interpretation of the selection rules for the angular momentum quantum number and for polarization in the Zeeman effect. On the assumption of light quanta, this principle led to attributing an angular momentum to the photons +h/2π or −h/2π, according to whether the light was circularly polarized to the right (σ+) or to the left (σ−), natural light being a mixture of the two types of photon.

Sambhu N. Datta

Abstract The solution of a unitarily transformed Dirac equation for the hydrogenic electron in zero magnetic field is investigated here. The momentum‐space representation is adopted as a natural recourse. The spinor part of the transformed wavefunction in momentum space can be easily prescribed for a central potential. Hence, for the Coulomb potential, a pair of equations is obtained for the radial components in momentum space. It is shown that starting from these radial equations, one can recover the equations previously derived by Rubinowicz, Lévy, and Lombardi for the problem of the Dirac hydrogen atom in momentum space. This establishes equivalence among different approaches based on the momentum representation, including the current treatment. The recovery of the equations due to Rubinowicz permits the exact eigenvalues to be written down and exact expressions to be derived for the radial components of the transformed wavefunction in momentum space. A new approach is adopted to carry out a reduction to the nonrelativistic regime and the nonrelativistic limit. At first the transformed momentum‐space equation for the hydrogen atom is rewritten in terms of the hyperspherical coordinates. The zeroth‐order solutions of the new equation are recovered in the limit c → ∞ where c is the speed of light. These are manifestly separable into positive‐ and negative‐energy forms. For positive energy, these solutions have nonvanishing upper components that are two‐component spinors. The latter exactly correspond to the single‐component, nonrelativistic, momentum‐space solutions derived by Fock. It is shown that when the upper component is corrected through first order in v2/c2 but the separability is still maintained for the transformed wavefunction, one retrieves the Pauli equation in momentum space. It is also shown that for a hydrogen atom placed in a uniform magnetic field, the nonvanishing momentum‐space matrix elements representing the anomalous Zeeman effect have a simple form, namely, the product of a radial integral and an angular integral. These integrals are equal to the well‐known radial and angular integrals in coordinate representation. The matrix elements can be easily evaluated. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003