Showing papers on "Configuration space published in 1969"
TL;DR: In this paper, the configuration space approach to the three-particle problem is generalized to the case of four particles, and special coordinates are defined which have simple symmetry properties with respect to the exchange of identical particles.
Abstract: The configuration‐space approach to the three‐particle problem is generalized to the case of four particles. Special coordinates are defined which have simple symmetry properties with respect to the exchange of identical particles. The construction of a suitable orthogonal system is discussed. Some of these functions are given explicitly. It is pointed out that the use of this orthogonal system leads to a considerable simplification for a large number of four‐particle problems, namely, the approximate reduction of the Schrodinger equation to a finite system of coupled differential equations for functions that depend on one variable only.
48 citations
TL;DR: In this article, the authors studied the geometric properties of the limiting high-compression regions (polytopes) for rods, disks, and spheres, and provided a connection between the moments of inertia of the polytopes (regarded as solid homogeneous bodies) and crystal elastic properties.
Abstract: The available configuration space for finite systems of rigid particles separates into equivalent disconnected regions if those systems are highly compressed. This paper presents a study of the geometric properties of the limiting high-compression regions (polytopes) for rods, disks, and spheres. The molecular distribution functions represent cross sections through the convex polytopes, and for that reason they are obliged to exhibit single-peak behavior by the Brunn-Minkowski inequality. We demonstrate that increasing system dimensionality implies tendency toward nearest-neighbor particle-pair localization away from contact. The relation between the generalized Euler theorem for the limiting polytopes and cooperative “jamming” of groups of particles is explored. A connection is obtained between the moments of inertia of the polytopes (regarded as solid homogeneous bodies) and crystal elastic properties. Finally, we provide a list of unsolved problems in this geometrical many-body theory.
25 citations
TL;DR: In this article, general rules for Feynman-parameter representations are given for both momentum-and configuration-space Feynmann diagrams, applicable to derivative couplings, spin-endowed propagators, as well as simpler cases.
Abstract: Completely general rules for Feynman-parameter representations are given for both momentum- and configuration-space Feynman diagrams. They are applicable to derivative couplings, spin-endowed propagators, as well as simpler cases. All quantities appearing in these representations are interpreted in terms of network analogies. The application to the determination of asymptotic limits of Feynman integrals with spin is considered on an example.
24 citations
TL;DR: In this article, a single-particle propagator for a free electron in a uniform electric field is presented, in its time-dependent form, taking simple closed forms in both momentum and configuration space.
Abstract: A calculation is presented of the single-particle propagator for a free electron in a uniform electric field. In its time-dependent form this takes simple closed forms in both momentum and configuration space. Series expansions for the Fourier transform of the configuration-space propagator are given. Using the latter a calculation is made of the electric-field dependence of the (approximate) bound state of the delta-function potential. A variational method which is suitable for general potentials is also given.
23 citations
TL;DR: In this article, the wave function of the α particle was expanded in terms of a complete set of nonspurious four-particle harmonic-oscillator states that are symmetric under the exchange of the nucleons and have orbital angular momentum zero.
22 citations
TL;DR: In this paper, the general projection technique for getting translationally-invariant configuration-space four-particle states of arbitrary symmetry and total orbital angular momentum, out of harmonic-oscillator states in the single relative coordinates was determined.
17 citations
TL;DR: In this paper, it is proved within the framework of nonrelativistic quantum mechanics that identical particles are either boson or fermions, and the starting assumptions are: (a) if ψ(x1, xn) is in the space H of allowed states, then so is Pψ for every permutation P; (b) |Pψ|2 = |ψ |2 for all ψ∈H, all allowed configurations (x1 … xn), and all ω∈ H; (c) H
Abstract: It is proved within the framework of nonrelativistic quantum mechanics that identical particles are either boson or fermions. The starting assumptions are: (a) if ψ(x1 … xn) is in the space H of allowed states, then so is Pψ for every permutation P; (b) |Pψ|2 = |ψ|2 for all ψ∈H, all allowed configurations (x1 … xn), and all ψ∈H; (c) H is a vector space (principle of superposition); (d) every ψ∈H is continuous along every path in the n‐particle configuration space C; and (e) there is at least one physical observable connecting each pair of irreducible components of C.
15 citations
TL;DR: In this article, a charge-conjugation transformation from the Green-Volkov algebra to the usual Fermi-field with "isospin" symmetry is introduced.
14 citations
TL;DR: In this paper, the total configuration space of the shell model for N particles can be broken into several subspaces which differ between themselves by the number of particles being in a pair state.
14 citations
TL;DR: In this article, the Jacobi metric was introduced to cover the non-smooth case of geodesic flows and Riemannian geodesics, which is the case in which the smoothness assumption was removed to guarantee existence of the flow.
Abstract: As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In face, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q -space or the configuration space), we may define a smooth function T_g on the cotangent bundle T^*M (q -p -space, or phase space). This function is the kinetic energy of q , and locally is given by
T_g(q, p) = gij(q) P_i P_j
Where q = (q^1,..., q^n) and p = (p_1,..., p_n) and g has components g^(ij).
Using T_g as a Hamiltonian function, the associated flow (that is, the global solution of Hamiltonian's equations) is exactly the geodesic flow; geodesics are obtained by projection to M .
Conversely, Hamiltonian motion in a potential V and metric g , that is, H = T_g + V , may be thought of as geodesic motion using the metric (e - V)g if e > V(q) . This new metric is called the Jacobi metric.
Traditionally, the theory of classical mechanics and Riemannian geometry always assumes g and V are smooth functions. However, the most elementary examples in fact are not smooth. One of the main reasons for the smoothness assumption was to guarantee existence of the flow (geodesics). This objection has now been removed.
The purpose of this note is to explain in an expository fashion what changes are necessary in the above theory to cover the non-smooth case. This new situation is quite different, although some interesting observations can be made.
8 citations
TL;DR: In this article, the predictions of the di-proton model and the kinetic energy approximation for the (p, 2p) reaction are compared and uncertainties introduced in these calculations due to various approximations and ambiguities are estimated.
TL;DR: In this article, the elastic and inelastic scattering cross sections for the reaction 15 N(n, n′) 15 N ∗ were calculated from 0-12 MeV using the method of coupled channels within a 1 particle-1 hole configuration space.
TL;DR: The implications of exact conformal symmetry for the S matrix of spinless massless particles are studied in this article, where explicit forms for the scattering amplitudes are obtained in configuration space.
Abstract: The implications of exact conformal symmetry for the S matrix of spinless massless particles are studied. Explicit forms for the scattering amplitudes are obtained in configuration space. Differential conditions for conformal‐invariant amplitudes are derived in momentum space. These are solved for the case of elastic two‐body scattering and lead to an integral representation of the general two‐body amplitude in terms of Lorentz scalars. The integral representation involves two arbitrary functions of two variables and four explicit quadratures. Further study of the four quadratures appears in appendices.
TL;DR: In this article, it was shown that the two usual definitions of microcanonical entropy are simply related to a single quantity, i.e., the volume enclosed, in configuration space, within the equipotential energy surface.
TL;DR: In this paper, it was shown that space-time can be regarded as a 4-dimensional subspace of a conformally flat, 6-dimensional space, or of a flat, 8dimensional space.
Abstract: It is shown that space-time can be regarded as a 4-dimensional subspace of a conformally flat, 6-dimensional space, or of a flat, 8-dimensional space The group of isometries of the tangent spaces
TL;DR: In this paper, the configuration space is divided into two regions by a closed surface which is chosen in such a way that the interactions between the nucleons in the outside region, in fact, can be regarded as negligible except for the Coulomb force.