Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education     

Intracavity laser polarization spectrometer for biomolecule traces

A polarization variant of an intracavity laser spectrometer based on the competition of beams in an argon ion laser, radiating a number of narrow lines in the 275 to 529 nm spectral range, is proposed and described for the spectral analysis of liquid samples, having broad absorption bands, mainly biomolecules in solutions. By careful optimization of the operating conditions, a procedure has been established that results in a minimal measurable absorbance decreased up to 10(-5) units of optical density. The examined spectrometer provides a wide dynamic range of analysis. A determination of trace contents of amino acids in methanol were carried out.     

Intracavity laser atomic absorption spectrometry with graphite furnace atomizer or pulsed laser sampler

An absorption intracavity laser spectrometer with two types of sample vaporization systems (graphite furnace electrothermal atomizer or laser sampler) is described that can be used for the determination of trace amounts of metals (Al, Cr, Fe and Mn) in liquid samples and at the surface of solid targets. The limits of detection for the elements tested are lower than those obtained by modern conventional spectrometers. The examined technique provides a wide dynamic range of linear standard calibration curves.     

Quantum chemical study of the tautomerism, geometry, and electronic structure of 1,2,3- and 1,2,4-triazoles

A systematic study was carried out on the tautomerism and geometry of 1,2,3- and 1,2,4-triazoles using the semiempirical AM1, PM3, MNDO, and MINDO/3 methods and nonempirical quantum chemical methods taking account of electronic correlation (MP2). The semiempirical methods were found to give incorrect results for the tautomerism of these triazoles, while the nonempirical methods correctly give the energy relationships and show enhanced stability for 2H-1,2,3- and 1H-1,2,4-triazoles attributed to the interaction of the unpaired electron pairs of the adjacent nitrogen atoms. Optimization of the geometry of 2H-1,2,3-triazole by the nonempirical methods showed that bases such as 6-21G and more expanded bases must be used and that electronic correlation should be taken into account. The use of updated calculation methods in the case of 1H-1,2,4-triazole did not give improved results.Prof. Asen Zlatarov University, 8010 Burgas, Bulgaria. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 645–651, May, 1998.     

Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential

We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essential-spectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V L ^m/2( ^m ) for m 3) and arbitrary A, or slowly decaying V (i.e. V(x |x|^– , (0,2), as |x| ) and magnetic potentials A corresponding to constant magnetic fields B = curl A.Partially supported by the Ministry of Culture, Science and Education under Grant No. 52.     

Intracavity laser polarization spectrometer for biomolecule traces

A polarization variant of an intracavity laser spectrometer based on the competition of beams in an argon ion laser, radiating a number of narrow lines in the 275 to 529 nm spectral range, is proposed and described for the spectral analysis of liquid samples, having broad absorption bands, mainly biomolecules in solutions. By careful optimization of the operating conditions, a procedure has been established that results in a minimal measurable absorbance decreased up to 10^–5 units of optical density. The examined spectrometer provides a wide dynamic range of analysis. A determination of trace contents of amino acids in methanol were carried out.