No abstract available

[en] Let (-Λ + V - E)PSI = 0 in Ωsub(R) = (x element Rsup(n): |x| >= R), PSI element L² (Ωsub(R)) where V = V₁(|x|) + V₂(x) and E<0, and let (-Λ + V₁(|x|) - E)v(|x|) = 0 for |x| >= R' >= R sufficiently large with v>0. It is supposed that E<0 and that V tends to zero in some sense as |x| → infinity. Conditions on V are given, so that for |x| large 0 < csub(-) <= (∫ |PSI(r,ω)|² dω)sup(1/2) / v(r) <= csub(+) < infinity where r=|x|, ω=x/|x| and dω denotes integration over the unit sphere. Also it is proved, that, given certain conditions on V₂(x), PSI(r,ω)/v(r), considerd as a function in ω with r fixed, has Hoelder-continuous ksup(th) derivatives in ω. This result holds uniformly in r for r>=R'. The conditions on V(x) include e.g. Hamiltonians describing one electron in the field of fixed nuclei or the case of short range potentials, i.e. |V(x)| <= Crsup(-1-epsilon) for |x| large, epsilon>0. (Author)

[en] Einstein's objections to the indeterminism of quantum mechanics are discussed

No abstract available

[en] Collapses of wave functions CWF by irreversible complex quanta systems are described. The CWFs may occur inside physical systems. Such processes take place by evolution of gas atoms wave functions. The CWS are manifested by normal external measurements, whereby the functions of the measured microobjects and those of the measurement device are collapsing simultaneously. Refs. 37

[en] A series of 12 lectures on quantum mechanics and its inter-pretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradoxon; Bell's inequations; interpretations of quantum theory; the role of the observer and the wave function of the world. 40 refs., 11 figs. (qui)

[en] Recently it was conjectured that nodal domains of random wavefunctions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wavefunction correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wavefunctions belong to the same universality class as non-correlated critical percolation. Second, we argue that level domains of random wavefunctions are described by the non-critical percolation model

[en] We study the case where g tends at timelike infinity to a stationary metric, we prove some existence theorems in spaces of solutions with finite energy for all times, and also with finite s-order energy

[en] The numerical quality of the ³H wave function obtained by the separable expansion method of Ernst, Shakin, and Thaler is examined. Separable approximations to the Paris potential with increasing accuracy are used in the ¹S₀ and ³S₁-³D₁ partial waves to calculate the binding energy, wave function, wave-function component percentages, and the S- and D-wave asymptotic normalization constants of ³H. The results are compared with existing five-channel calculations obtained directly (without expansion) from the Paris potential to determine convergence. It is found that the results converge rapidly to the right values, indicating that the ³H wave function thus obtained is of high quality and essentially indistinguishable from that obtained directly from the Paris interaction. (authors)

[en] In molecular systems containing conical intersections (CIs), a nontrivial geometric phase (GP) appears in the nuclear and electronic wave functions in the adiabatic representation. We study GP effects in nuclear dynamics of an N-dimensional linear vibronic coupling (LVC) model. The main impact of GP on low-energy nuclear dynamics is reduction of population transfer between the local minima of the LVC lower energy surface. For the LVC model, we proposed an isometric coordinate transformation that confines non-adiabatic effects within a two-dimensional subsystem interacting with an N − 2 dimensional environment. Since environmental modes do not couple electronic states, all GP effects originate from nuclear dynamics within the subsystem. We explored when the GP affects nuclear dynamics of the isolated subsystem, and how the subsystem-environment interaction can interfere with GP effects. Comparing quantum dynamics with and without GP allowed us to devise simple rules to determine significance of the GP for nuclear dynamics in this model