Equidistant spectra of anharmonic oscillators

Some representative potentials of the anharmonic-oscillator type are constructed. Some corresponding spectra-shift operators are also constructed. These operators are a natural generalization of Fok creation and annihilation operators. The Schrodinger problem for these potentials leads to an equidistant energy spectrum for all excited states, which are separated from the ground state by an energy gap. The general properties of the dynamic system generated by spectral-shift operators of third degree are analyzed. Several examples of such anharmonic oscillators are discussed. The relationship between the eigenvectors of the Schrodinger problem and a certain type of nonclassical orthogonal polynomials is established.     

Exactly soluble anharmonic potential models

The construction and exact quantum mechanical solution of anharmonic potential models is discussed. For low energy eigenvalues the proposed models simulate the usual quadratic-quartic potentials, but for high eigenvalues their properties are essentially those of the harmonic oscillator.     

On the energy spectra of one-dimensional anharmonic oscillators

In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE _n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω ² x ²+λx ^2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given.     

Near-infrared Fourier-transform and millimeterwave spectra of the BiS radical

This paper reports the 6400-7400 cm⁻¹ Fourier-transform (FT) near-infrared (NIR) emission spectrum of the BiS X₂²Π_3/2 → X₁²Π_1/2 fine structure bands as well as the millimeterwave rotational spectrum of the X₁²Π_1/2 state. For the FTNIR observations, BiS was produced by reaction of bismuth with sulfur vapor and excited by energy transfer from metastable oxygen, O₂(a¹Δ_g), in a fast-flow system. As was the case for BiO [O. Shestakov, R. Breidohr, H. Demes, K.D. Setzer, E.H. Fink, J. Mol. Spectrosc. 190 (1998) 28-77], the 0.5 cm⁻¹resolution spectrum revealed a number of strong bands in the Δv = 0 and ±1 sequences which showed perturbed band spacings, band shapes, and intensities due to avoided crossing of the X₂²Π_3/2 and A₁⁴Π_3/2 potential curves for v^′ ? 4 of X₂²Π_3/2. The millimeterwave rotational spectrum of BiS in its X₁²Π_1/2 state was observed when BiS was produced in a high-temperature oven by a discharge in a mixture of Bi vapor and CS₂. The signal to noise ratio was markedly improved by using a White-type multipath cell. Ninety seven features from J′ = 23.5 to J′ = 41.5 were measured between 150 and 300 GHz. Analysis of the 0.5 cm⁻¹ resolution FT spectrum yielded the fine structure splitting and vibrational constants of the states. A simultaneous analysis of millimeterwave and a 0.005 cm⁻¹ FT spectrum of the 0-0 band of the NIR system was carried out to give precise rotational, fine, and hyperfine constants for the X₁²Π_1/2 and X₂²Π_3/2 states. The results are consistent with those reported earlier for BiO and indicate only a slight decrease in the unpaired electron density in the 6p(π^∗) orbital on the Bi atom.     

Finite discontinuities in the energy eigenvalue spectra of anharmonic oscillators

The existence of finite discontinuities in the energy eigenvalue spectra of certain multiterm potentials when their coupling parameters attain suitably chosen limiting values has been reported in the literature. We show that such discontinuities are also characteristic of such well-known systems as generalized anharmonic oscillators and the doubly anharmonic oscillator in one dimension. The present study strengthens the general conjecture that eigenvalue spectra are likely to display discontinuities in situations where a potential undergoes an abrupt change in shape with smooth variation of its coupling parameters.     

Partition function for anharmonic potential by path-integral method

We present here an improved calculation of the partition function in the frame work of Feynman's path-integral formalism, and as its application derive an expression for the Helmholtz free energy of a one dimensional anharmonic potential non-perturbatively up to the quartic term in the potential.     

Near-infrared spectra of hydrogen-bonded cyclic dimers of some carboxylic acids

Near-infrared spectra in the 3900–11000 cm⁻¹ region were measured for formic and acetic acids and also for their deutero analogs in the gaseous state at various temperatures. Observed monomer and dimer bands were assigned to overtone and summation bands of various vibrational modes. Special attention was paid to the first overtone bands of the OH and OD stretching modes of the hydrogen-bonded cyclic dimers, which were observed at ∼5930 cm⁻¹ and ∼5870 cm⁻¹ for formic-d acid and acetic-d₃ acid, respectively, and also at ∼4370 cm⁻¹ for acetic acid-d. On the basis of these data the anharmonicity constants were calculated for the OH and OD stretching modes and were found to increase by hydrogen-bond formation in the gaseous state. Hydrogen-bonded overtone bands are broad and have submaxima with intervals nearly half of those of the OH and OD fundamental bands. The results concerning the band breadths of the OH and OD stretching vibrations of the dimers were interpreted on the line of the idea that they strongly couple with the O?O stretching vibration.     

Determination of the anharmonic potential of some linear molecules

The coefficients of the anharmonic potential (a polynomial of fourth degree in the generalized coordinates) of the linear molecules CO₂, HCN, and C₂H₂ are calculated. A simple (linear) scheme of calculation is proposed and tested. The spectra of higher orders are satisfactorily reproduced.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 65–67, July, 1980.     

Analysis of vibrational spectra of methyl-substituted uracils in the anharmonic approximation

We have analyzed the vibrational spectra of uracil and its methyl-substituted derivatives using the DFT/B3LYP/6-31G(p,d) method, in the anharmonic approximation. We have shown that it is possible to use second-order anharmonic theory of vibrational spectra in predictive calculations for substituted uracils. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 431–436, July–August, 2006.     

Bound diffusion of ultrafine particles in generalized anharmonic potential

Bound diffusion of ultrafine particles of ferric hydroxide precipitated inside the polymeric cross-linkage degree the experimental spectra reveal a striking broadening up to hundreds of mm/s. This is a consequence of the crossover from the diffusion of a Brownian oscillator to free diffusion in restricted volume, the spatial displacements of the particles depending on the cross-linkage and changing from 0.1 to 0.6 Å.     

A lineshape of the trapped particle in anharmonic potential

The line of resonance absorption of an atom in a gas usually suffers Doppler broadening. It has been first shown that the particle trapped in an anharmonic potential emits a narrow line with no Doppler broadening.     

ESCA applied to liquids. II. Valence and core electron spectra of formamide

A brief review of the technique of applying ESCA to liquid samples is given. A list of solvents suitable for ESCA studies is presented and the particul     

Deterministic escape of a dimer over an anharmonic potential barrier

In the present paper we consider the deterministic escape dynamics of a dimer from a metastable state over an anharmonic potential barrier. The underlying dynamics is conservative and noiseless and thus, the allocated energy has to suffice for barrier crossing. The two particles comprising the dimer are coupled through a spring. Their motion takes place in a two-dimensional plane. Each of the two constituents for itself is unable to escape, but as the outcome of strongly chaotic coupled dynamics the two particles exchange energy in such a way that eventually exit from the domain of attraction may be promoted. We calculate the corresponding critical dimer configuration as the transition state and its associated activation energy vital for barrier crossing. It is found that there exists a bounded region in the parameter space where a fast escape entailed by chaotic dynamics is observed. Interestingly, outside this region the system can show Fermi resonance which, however turns out to impede fast escape.     

A comparative ab initio study of the structures,dipole moments,force fields,and anharmonic frequencies of formamide and thioformamide

The structures, dipole moments, force fields, and anharmonic frequencies for the planar conformation of formamide and thioformamide were calculated using the unscaled 4-31G basis set, augmented with a full set of d functions on the sulfur, and full geometry optimization. Extensive comparison of the geometries are made, especially the CO and CS bond lengths, with both the experimental values for the amides and values calculated in previous studies on the acids and other carbonyl compounds. Comparison of the dipole moments calculated using the optimized and experimental geometries with the experimental values suggest there is some inconsistancy in the experimental geometry for thioformamide. Quadratic, cubic, and quartic force constants are calculated for both amides, and hence the fundamental vibration frequencies. Critical comparisons are made with the assignments based on experimental observations. Differences in the bond lengths and stretching force constants for the two NH bonds are shown to be consistent with a hydrogen-bonding type of interaction between the proximal NH and CO and CS groups, like that in the acids.     

Near-infrared ultrabroadband luminescence spectra properties of subvalent bismuth in CsI halide crystals

We observed two ultrabroadband near-infrared (NIR) luminescence bands around 1.2 and 1.5 μm in as-grown bismuth-doped CsI halide crystals, without additional aftertreatment. Dependence of the NIR emission properties on the excitation wavelength and measurement temperature was studied. Two kinds of NIR active centers of subvalent bismuth and color centers were demonstrated to coexist in Bi:CsI crystal. The eye-safe 1.5 μm emission band with an FWHM of 140 nm and lifetime of 213 μs at room temperature makes Bi:CsI crystal promising in the applications of the ultrafast laser and ultrabroadband amplifier.     

Direct determination of the anharmonic vibrational potential for H in Pd

The vibration spectra of and -phase PdH(D)_x have been measured by neutron inelastic scattering. From a detailed analysis of the spectra, we conclude that the potentials for hydrogen and deuterium are very similar and strongly anharmonic. The results show definitively that anharmonicity is the principal contribution to the anomalous isotope dependence of the superconducting transition temperature in PdH(D).     

Energy eigenvalues for anharmonic and double-well oscillators with even power polynomial potential

Energies for different states of anharmonic and double-well oscillators described by V(x) = Σ_{j = 1}^s(a_2j/2j)x^2j have been determined using the renormalized hypervirial-Padé scheme. A comparison of the results with available exact values shows that the method is quite successful for anharmonic oscillators but fails in the case of double-well oscillators. Also included is the discussion of the dependence of the energy on various parameters.