scholarly journals Oscillator Representation and Generalized van der Waals Hamiltonians

1997 ◽  
Vol 12 (16) ◽  
pp. 1193-1207
Author(s):  
M. Dineykhan
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Ground State ◽  
Van Der Waals ◽  
Bound State ◽  
Oscillator Strengths ◽  
Uniform Electric Field ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The oscillator representation method is extended to calculate the energy spectrum of bound state systems described by axially symmetrical potentials in the parabolic system coordinates. In particular, it is applied to calculate the energy of the ground and excited states of the hydrogen atom in the uniform electric field and van der Waals field. The method gives the perturbation formulas for the analytic spectrum of the hydrogen atom in the generalized van der Waals field and defines oscillator strengths for transitions from the ground state to the perturbed manifold n=10, m=0.

scholarly journals MESIC MOLECULES OF LIGHT NUCLEI IN THE OSCILLATOR REPRESENTATION

1994 ◽  
Vol 09 (23) ◽  
pp. 2083-2095
Author(s):  
M. DINEYKHAN ◽  
G.V. EFIMOV
Keyword(s):  
Ground State ◽  
Hydrogen Isotopes ◽  
Binding Energies ◽  
Critical Values ◽  
Light Nuclei ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The mesic molecules (HμNZ), where H is the hydrogen isotopes (p, d, t) and NZ are nuclei with charges Z=2, 3, 4, …and masses MZ=2Zmp, are studied. The energy values of the ground state for the mesic molecules of light nuclei have been calculated by using the oscillator representation method. The dependence of the binding energies of the muonic molecules on nuclear charges and the critical values of nuclear charges are obtained.

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

The ground state and low-lying excited states of CCCN radical and its ions: a CASSCF/CASPT2 study

2016 ◽  
Vol 94 (9) ◽  
pp. 803-807
Author(s):  
Angyang Yu
Keyword(s):  
Excited States ◽  
Ground State ◽  
Linear Structure ◽  
Electronic Configuration ◽  
Geometric Optimization ◽  
Oscillator Strengths ◽  
Basis Set ◽  
Excitation Energies ◽  
Complete Active Space ◽  
Vertical Excitation

The ground state and low-lying excited states of the CCCN radical and its ions have been investigated systematically using the complete active space self-consistent field (CASSCF) and multi-configuration second-order perturbation theory (CASPT2) methods in conjunction with the ANO-RCC-TZP basis set. The calculated results show that the state 12Σ+ has the lowest CASPT2 energy among the electronic states. By means of the geometric optimization of this radical, it could be found that the molecule exhibits linear structure, with the bond lengths R1 = 1.214 Å, R2 = 1.363 Å, R3 = 1.162 Å, which are very close to the experimental values. The calculated vertical excitation energies and the corresponding oscillator strengths show that there are three relatively strong peaks at energies 0.63, 4.04, and 5.49 eV, which correspond to the transitions 12Σ+ → 12Π, 12Σ+ → 22Π, and 12Σ+ → 22Σ+, respectively. Additionally, the electronic configuration and the harmonic vibration frequencies of each state are also investigated.

MR-CISD and MR-AQCC Calculation of Excited States of Malonaldehyde: Geometry Optimizations Using Analytical Energy Gradient Methods and a Systematic Investigation of Reference Configuration Sets

2003 ◽  
Vol 68 (3) ◽  
pp. 447-462 ◽  
Author(s):  
Silmar A. do Monte ◽  
Michal Dallos ◽  
Thomas Müller ◽  
Hans Lischka
Keyword(s):  
Excited States ◽  
Ground State ◽  
Transition Energy ◽  
Gradient Methods ◽  
Systematic Investigation ◽  
Oscillator Strengths ◽  
Excitation Energies ◽  
Band Maximum ◽  
Vertical Excitation ◽  
Energy Gradient

Extended MR-CISD and MR-AQCC calculations have been performed on the ground state and the first two excited states of malonaldehyde. Full geometry optimizations have been carried for Cs and C2v structures both at MR-CISD and MR-AQCC levels. Vertical and minimum-to-minimum excitation energies and oscillator strengths have been computed. Systematic studies have been undertaken concerning several types of reference spaces. Agreement with the experimental 0-0 transition energy to the S1 state (expt. 3.50 eV, calc. 3.56 eV) and for the vertical excitation to S2 (expt. band maximum 4.71 eV, best estimate 4.86 eV) is very good. In agreement with the CASSCF/CASPT2 results by Sobolewski and Domcke (J. Phys. Chem. A 1999, 103, 4494), we find that the hydrogen bond in malonaldehyde is weakened by excitation to the S1 state. The barrier for proton transfer in the S1 state is increased in comparison with the ground state.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

XXXVII.—The Van der Waals Force between a Proton and a Hydrogen Atom. II. Excited States

1948 ◽  
Vol 62 (3) ◽  
pp. 360-368 ◽  
Author(s):  
C. A. Coulson ◽  
C. M. Gillam
Keyword(s):  
Hydrogen Atom ◽  
Closed Form ◽  
Interaction Energy ◽  
Excited States ◽  
Internuclear Distance ◽  
Van Der Waals ◽  
Quantum States ◽  
Van Der Waals Force ◽  
Image Position

SummaryThe interaction energy, or Van der Waals force, between a proton and a hydrogen atom in any one of its allowed quantum states is calculated in terms of the internuclear distance R by an expansion of the formAll the coefficients up to and including E5 are obtained in closed form. For values of R for which the expansion is valid, the coefficients are determined absolutely, no approximations being introduced.

Excited State Absorption and Cross Sections for Er-Doped Glasses

1989 ◽  
Vol 172 ◽  
Author(s):  
S. Zemon ◽  
G. Lambert ◽  
W. J. Miniscalco ◽  
L. J. Andrews ◽  
B. T. Hall
Keyword(s):  
Excited State ◽  
Excited States ◽  
Cross Sections ◽  
Ground State ◽  
Excited State Absorption ◽  
Fiber Amplifiers ◽  
Oscillator Strengths ◽  
Ground State Absorption ◽  
Doped Glasses ◽  
Er Doped

AbstractPump-excited-state-absorption (ESA) measurements on Er3+-doped phosphates, fluorophosphates, and silicate bulk glasses indicate that ESA cross sections are approximately equal to ground state absorption (GSA) cross sections in the 800-nm band. The oscillator strengths of the ESA and GSA bands are also approximately equal, in qualitative agreement with Judd-Ofelt calculations. Fluorozirconate samples were found to have substantial populations in the upper excited states for the measurement conditions used and ESA transitions originating from four excited states were identified. Fluorozirconate fiber amplifiers and lasers at 1.55 μm, therefore, would have decreased efficiency for 800-nm pumping.

Compression effects on dipole transitions and state lifetimes for a hydrogen atom

2016 ◽  
Vol 94 (9) ◽  
pp. 894-901 ◽  
Author(s):  
A. Solórzano ◽  
N. Aquino ◽  
A. Flores-Riveros
Keyword(s):  
Boundary Condition ◽  
Hydrogen Atom ◽  
Excited States ◽  
Dirichlet Boundary ◽  
Numerical Technique ◽  
Oscillator Strengths ◽  
Quantum Mechanical ◽  
Mechanical Problem ◽  
Radial Schrödinger Equation ◽  
Compression Effects

The quantum mechanical problem of a hydrogen atom placed at the center of an impenetrable sphere of radius r0 is solved by using two different methods, where, in the first, a trial wave function, consisting of a hydrogen-like function times a cutoff factor that ensures fulfillment of Dirichlet boundary condition, is proposed, whereas in the second, the radial Schrödinger equation is solved by means of an accurate numerical technique. We computed the energies for the ground and first excited states of S-, P-, and D-symmetry, as well as dipole transitions, oscillator strengths, and a few state lifetimes. Although the variational method and the numerical solution are found to give similar qualitative behaviours, which, in general, compare reasonably well with some results published previously, the 2p state lifetimes obtained in the present calculations appear to be at variance with the latter at some particular box radii.

PERTURBED WAVEFUNCTIONS OF THE EXCITED STATES OF HYDROGEN ATOM IN STARK EFFECT

1994 ◽  
Vol 08 (06) ◽  
pp. 727-740 ◽  
Author(s):  
G. K. SAPRA ◽  
V. S. BHASIN ◽  
L. S. KOTHARI
Keyword(s):  
Hydrogen Atom ◽  
Electric Field ◽  
External Electric Field ◽  
Excited States ◽  
Ground State ◽  
Stark Effect ◽  
Second Order ◽  
Electric Polarizability ◽  
Perturbation Equations

We extend the procedure originally suggested by Dalgarno and Lewis in studying the second-order Stark effect for the ground-state hydrogen atom to the excited states. We solve the perturbation equations for the excited states of hydrogen atom placed in an external electric field to obtain expressions for the perturbed wavefunctions. Here the emphasis is on studying in detail the nature of the perturbed wavefunction rather than energy shifts as investigated in most of the attempts made so far. The effect of the electric field on these wavefunctions is analysed and the values of the electric polarizability of the hydrogen atom in the excited states obtained in this way are compared with the earlier work.

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