One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Reaction of Copper(II) Chloroacetate with Pyrazole. Synthesis of a One-Dimensional Coordination Polymer and Unexpected Dehydrochlorination Reaction

The reaction of copper(II) chloroacetate (1d) with pyrazole (Hpz) mainly yielded the mononuclear compound [Cu(μ-ClCH2COO)2(Hpz)2] (2m), which self-assembled generating a one-dimensional coordination polymer. Moreover, the concomitant isolation of the tetranuclear [{Cu2(μ-pz)(μ-OCH2COO)(Hpz)(MeOH)}2(μ-ClCH2COO)2] (3t) and hexanuclear [{Cu3(μ3-OH)(μ-pz)3(Hpz)2}2(μ-ClCH2COO)2](Cl)2 (4h) species evidenced the occurrence of a peculiar, previously unreported, dehydrochlorination reaction and the formation of the trinuclear triangular moiety [Cu3(μ3-OH)(μ-pz)3]. Theoretical calculations based on density functional theory including solvation effects indicate a possible pathway for the formation of 3t. Interestingly, besides the energy minimum corresponding to 3t, a further relative energy minimum is found for a species which can be considered a possible reaction intermediate.

Novel one-dimensional structures and solution behaviour of copper(II) bromide and chloride complexes of a new pentapyridyldiamine ligand

Copper(II) bromide and chloride complexes of the new heptadentate ligand 2,6-bis(bis(2-pyridylmethyl)amino)methylpyridine (L) have been prepared. For the bromide complexes, chains of novel, approximately C-2-symmetric, chiral [Cu-2(L)Br-2](2+) 'wedge-shaped' tectons are found. The links between the dicopper tectons and the overall chirality and packing of the chains are dictated by the bromide ion content, not the counter anion. In contrast, the chloride complexes exhibit linked asymmetric [Cu-2(L)Cl-3](+) tectons with distinct N3CuCl2 and N4CuCl2 centres in the solid. The overall structures of the dicopper bromide and chloride units persist in solution irrespective of the halide. The redox chemistry of the various species is also described.

Magic-angle effects in the interlayer magnetoresistance of quasi-one-dimensional metals due to interchain incoherence

The dependence of the magnetoresistance of quasi-one-dimensional metals on the direction of the magnetic field show dips when the field is tilted at the so-called magic angles determined by the structural dimensions of the materials. There is currently no accepted explanation for these magic-angle effects. We present a possible explanation. Our model is based on the assumption that, the intralayer transport in the second most conducting direction has a small contribution from incoherent electrons. This incoherence is modeled by a small uncertainty in momentum perpendicular to the most conducting (chain) direction. Our model predicts the magic angles seen in interlayer transport measurements for different orientations of the field. We compare our results to predictions by other models and to experiment.

Sodium 2-nitrocinnamate dihydrate: a one-dimensional hydrogen-bonded coordination polymer

The title compound catena-poly[aqua-mu3-2-nitrocinnamato], [Na(C9H6NO4)(H2O)2]n, the sodium salt of trans-2-nitrocinnamic acid, is a one-dimensional coordination polymer based on six-coordinate octahedral NaO6 centres comprising three facially-related monodentate carboxylate O-atom donors from separate ligands (all bridging)[Na-O, 2.4370(13)-2.5046(13)A] and three water molecules (two bridging, one monodentate) [Na-O, 2.3782(13)-2.4404(17)A]. The structure is also stabilized by intra-chain water-O-H...O(carboxylate) and O-H...O(nitro) hydrogen bonds.

One-dimensional hydrogen-bonded structures in the 1:1 proton-transfer salts of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine

The crystal structures of the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine, viz. diisopropylaminium 2-carboxy-4,5-dichlorobenzoate (1) and hexamethylenetetraminium 2-carboxy-4,5-dichlorobenzoate hemihydrate (2), have been determined. Crystals of both 1 and 2 are triclinic, space group P-1, with Z = 2 in cells with a = 7.0299(5), b = 9.4712(7), c = 12.790(1)Å, α = 99.476(6), β = 100.843(6), γ = 97.578(6)o (1) and a = 7.5624(8), b = 9.8918(8), c = 11.5881(16)Å, α = 65.660(6), β = 86.583(4), γ = 86.987(8)o (2). In each, one-dimensional hydrogen-bonded chain structures are found: in 1 formed through aminium N+-H...Ocarboxyl cation-anion interactions. In 2, the chains are formed through anion carboxyl O...H-Obridging water interactions with the cations peripherally bound. In both structures, the hydrogen phthalate anions are essentially planar with short intra-species carboxylic acid O-H...Ocarboxyl hydrogen bonds [O…O, 2.381(3) Å (1) and 2.381(8) Å (2)].