Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions. The corresponding photons statistics are discussed and some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys., Special Issue celebrating the 20th anniversary of quantum state engineering (R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201

OPYT PRIMENENIYa PROFILAKTIChESKOY DOZY ALENDRONATA (FOSAMAKS 35 mg) DLYa LEChENIYa OSTEOPOROZA u zhenshchin v postmenopauzes subklinicheskim tireotoksikozom

The aim was to estimate the effects of treatment with alendronate (Fosomax 35 mg) in postmenopausal women with osteoporosis and subclinical hyperthyroidism. Thirty postmenopausal women (64 (60-69) years old) with osteoporosis (T-score ≤ -2,5) and subclinical hyperthyroidism (77% with endogenous subclinical hyperthyroidism and 23% on L-thyroxine suppres-sive therapy after thyroidectomy due to differentiated thyroid cancer) were randomly assigned into two groups: 1-14 women received Fosamax 35 mg a week in combination with 500 mg of calcium and 400 UI of Vitamin D3 (VD) daily; 2-16 women received 1000 mg of calcium and 800 UI of VD daily. Euthyroidism was achieved in all women with endogenous subclinical hyperthyroidism. An increase in physical activity was recommended to all patients and a hypolipidemic diet was given to those who had had high cholesterol level. Biochemical parameters (calcium (Ca), phosphorous (P), creatinine (Cre), alkaline phosphatase (ALP), cholesterol, low density lipoprotein (LDL), high density lipoprotein (HDL), triglycerides (TG), cholesterol/HDL ratio) in fasting serum as well as calcium/creatinine ratio in fasting urine (U-Ca/U-Cre); biochemical markers of bone metabolism: osteocalcin (OC) and C-terminal telopeptide of type I collagen (b-CTx) serum ("ECLIA", Roche Elecsys 1010/2010), BMD (DXA; Prodigy, Lunar) at the lumbar spine (L1-L4), femoral neck (FN), total hip (TH) and radius total (RT) were measured at the baseline visit and after 1 year of treatment. At the baseline visit there were not found any differences between the 1 and the 2 groups. After 12 months of treatment the markers of bone metabolism as well as ALP decreased significantly in both groups, though the decreases were significantly greater (