[en] Seniority is shown to provide a guiding principle in the construction of physical bosons. Within the framework of a single j-shell physical boson operators are constructed using the Dyson mapping

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[en] A method is given of constructing new classes of potential V and corresponding wave functions in a closed analytical form uisng the known solutions to the Schroedinger equation with some potential V for energy E and angular momentum l along arbitrary lines in the (l + 1/2)²,E) plane. The Crum-Krein transformations which give solutions for fixed l and any E (or their modification for fixed E and different values l) are a particular case of the suggested formalism. (Auth.)

[en] For a Hamiltonian of the form H = (1)/(2) ( p-A(r,t))²+V(r,t), the conditions on the scalar and vector potentials V(r,t) and A(r,t) have been found such that there exists an exact invariant that is quadratic in each component of the canonical momentum p. The invariant is written in the form I(r,p,t) = (1)/(2) (f₂(r,t)xp-f₁(r,t))²+f₀(r,t), where f₂ is a nonsingular symmetric real dyad, f₁ is a real vector, and f₀ is a real scalar. For the cases in which f₂ is proportional to the unit dyad, or the vector potential is identically zero and f₂ commutes with the time derivative of f₂, all of the potentials that satisfy the conditions for such invariants to exist have been found explicitly and the invariants have been found in terms of the potentials. The derivation is a generalization of a method reported by Lewis and Leach for the corresponding one-dimensional problem. For the case in which the vector potential vanishes identically, the result is a generalization of a result found in three dimensions by Chandrasekhar. The results presented are applicable in plasma physics and stellar dynamics

[en] A variational solution to a model problem of a hydrogen atom near a sharp planar surface of a semi-infinite substrate is studied. Results are presented for the ground and excited eigenstates and dipole moments of the hydrogen atom as a function of distance from the surface for two models: (a) a system in which the half-space occupied by the solid is represented by an infinite potential step; and (b) a system in which the semi-infinite substrate is perfectly imaging subject to a boundary condition that excludes the atomic electron from the substrate. Model (b) is considered as an idealized model for physisorption, where the exclusion of the electron simulates the exchange repulsion originating from the overlap of the atomic and substrate electrons. Results for the physisorption holding potential as a function of distance from the plane are presented and discussed

[en] The standard s-state Potts model is generalized to a model defined on plaquettes of Zsup(d), and the s->1, 0 limits are shown to correspond to plaquette percolation and percolation of plaquette trees, respectively. The model is further extended to r-cells (cubes, hypercudes, etc). On Zsup(d) and the s->1, 0 limits are exhibited. (orig.)

[en] An alternative exact-path-integral treatment of the hydrogen atom is proposed. The earlier treatment is based on the bijective transformation of Kustaanheimo and Stiefel. The proposed procedure reduces the radial path integral for the hydrogen atom into that for an oscillator in R³ by one-to-one mapping. (orig.)

[en] The Bell inequalities, being derived for micro-systems, cannot be tested by (macroscopic) experiments without additional assumptions. A macroscopic definition of local realism is proposed which might be the starting point for deriving Bell inequalities testable without auxiliary assumptions. (orig.)

[en] The general solution to finding the continuous QND observables of a given system is obtained. The method is also extended to finding the QNDF observables of the system. An example is given, using the harmonic oscillator. (orig.)

[en] We consider self-adjoint realizations of Schroedinger operators: Hsub(ω)=-d²/dt² + qsub(ω)(t) depending on a parameter ω running through a probability space. (orig./HSI)