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Construction of a complete orthogonal system for the quantum-mechanical three-body problem
ABSTRACTS
The principle of compensation of dangerous diagrams is applied when combined with the quasi particle self-energy to second order, linear integral equations coupling the energy gap and the single equations are solved for a singlet state shell-type interaction.
189 to second order which, gives a set of two nonparticle energy. These
Construct.ion of d Complete Orlhogonul System fog the QauntumMechanical Three-Body Probiem. WERNER ZICKENDKAHT, Institut fur Mat.hematische Physik, Technische Hochschule Karlsrrthe, Germany. A coordinate system with simple symmetry properties is described which is suitable for the treatment of the quantum-mechanical three-body problem. The Schr6dinger equation for spinless particles is transformed to these coordinates and the orbital angular momentum is separated out reducing the Schrodinger equation to a system of coupled differential equations involving only three internal coordinates. A special interaction for the three-body system is introduced, for which the system of coupled differential equations can be solved. The solui ions form a complete orthogonal system of functions for the internal degrees of freedom. Explicit solutions are given for orbital angular momenta 0, 1, 2. The usefulness of the method is demonstrated for the groundstate of the helium atom. Spin and Crnitary Spin Independence in SLi(8) Symmetry. S. Iw.\o, Institut fur Theoretische Physik der Universitat, Bern, Switzerland. Theory of SL:(sj symmetry model in the spin and unitary spin independence for elementary part,icles is developed. The classification of the meson and baryon states in the subgroup sr;(4j SC7(2) is discussed and a possible assignment to the observed states is given. The assignment given here will be verified when we observe the doubly charged mesons and triply charged baryon etc. The mass differences and various decay rates of mesons with both odd and even parity are calculated and compared with the available information. The sizes of the anomalous magnetic moments of quart.ets must be identical. The result of our theory is compared with SCr(4) and SC’(G) predictions. The detailed measurement of the suggested radiative decay rates of known mesons will distinguish the validity between SIT(G) and SI.r(8) theory. The “charm-changing” weak current is introduced into the weak interaction in conformity with the Cabibbo current. The strength of the additional weak cllrrent thlls introduced can be determined as to explain the apparent discrepancy between the muon and the neutron be&decay coupling constant. Asymptotic
Solution o.f the Schriidinger Equation for the Three-Uody Problem. J)AVID J. New York University, Conrant Institute of Mathematical Sciences, New York, S. I. RUBINOW, Cornell University, Graduat,e School of Medical Sciences, New York, N. Y. and Sloan-Kett,ering Institute for Cancer Research, New York, N. Y. The W. K. B. method is applied to determine the asymptotic expansion of the SchrGdinger wave function for a system of three spinless particles which interact through central forces. A new assumption is made concerning the form of the asymptotic wave function. This is designed to take advantage of the fact t.hat the total angular momentum of the system is constant. As a result, new equations for the phase and amplitltde of the wave function, different from those which follow from ordinary W. K. B. theory, are obtained. In particular, the phase function satisfies a Hamilton-Jacobi-like equation of degree 2(2L + 1). The method is applied to the helium atom for S- and P-states. The wave functions and energy eigenvalues are determined by means of perturbation theory. A classical description of the various electronic motions in the helium atom is presented. Previous attempts to describe the helium atom in terms of the old Bohr theory are clarified. VEZZE~TTI, Ir;. Y. AND
The principle of compensation of dangerous diagrams is applied when combined with the quasi particle self-energy to second order, linear integral equations coupling the energy gap and the single equations are solved for a singlet state shell-type interaction.
189 to second order which, gives a set of two nonparticle energy. These
Construct.ion of d Complete Orlhogonul System fog the QauntumMechanical Three-Body Probiem. WERNER ZICKENDKAHT, Institut fur Mat.hematische Physik, Technische Hochschule Karlsrrthe, Germany. A coordinate system with simple symmetry properties is described which is suitable for the treatment of the quantum-mechanical three-body problem. The Schr6dinger equation for spinless particles is transformed to these coordinates and the orbital angular momentum is separated out reducing the Schrodinger equation to a system of coupled differential equations involving only three internal coordinates. A special interaction for the three-body system is introduced, for which the system of coupled differential equations can be solved. The solui ions form a complete orthogonal system of functions for the internal degrees of freedom. Explicit solutions are given for orbital angular momenta 0, 1, 2. The usefulness of the method is demonstrated for the groundstate of the helium atom. Spin and Crnitary Spin Independence in SLi(8) Symmetry. S. Iw.\o, Institut fur Theoretische Physik der Universitat, Bern, Switzerland. Theory of SL:(sj symmetry model in the spin and unitary spin independence for elementary part,icles is developed. The classification of the meson and baryon states in the subgroup sr;(4j SC7(2) is discussed and a possible assignment to the observed states is given. The assignment given here will be verified when we observe the doubly charged mesons and triply charged baryon etc. The mass differences and various decay rates of mesons with both odd and even parity are calculated and compared with the available information. The sizes of the anomalous magnetic moments of quart.ets must be identical. The result of our theory is compared with SCr(4) and SC’(G) predictions. The detailed measurement of the suggested radiative decay rates of known mesons will distinguish the validity between SIT(G) and SI.r(8) theory. The “charm-changing” weak current is introduced into the weak interaction in conformity with the Cabibbo current. The strength of the additional weak cllrrent thlls introduced can be determined as to explain the apparent discrepancy between the muon and the neutron be&decay coupling constant. Asymptotic
Solution o.f the Schriidinger Equation for the Three-Uody Problem. J)AVID J. New York University, Conrant Institute of Mathematical Sciences, New York, S. I. RUBINOW, Cornell University, Graduat,e School of Medical Sciences, New York, N. Y. and Sloan-Kett,ering Institute for Cancer Research, New York, N. Y. The W. K. B. method is applied to determine the asymptotic expansion of the SchrGdinger wave function for a system of three spinless particles which interact through central forces. A new assumption is made concerning the form of the asymptotic wave function. This is designed to take advantage of the fact t.hat the total angular momentum of the system is constant. As a result, new equations for the phase and amplitltde of the wave function, different from those which follow from ordinary W. K. B. theory, are obtained. In particular, the phase function satisfies a Hamilton-Jacobi-like equation of degree 2(2L + 1). The method is applied to the helium atom for S- and P-states. The wave functions and energy eigenvalues are determined by means of perturbation theory. A classical description of the various electronic motions in the helium atom is presented. Previous attempts to describe the helium atom in terms of the old Bohr theory are clarified. VEZZE~TTI, Ir;. Y. AND