Perturbed energy eigenvalues of the Salpeter equation in the oscillator-representation method

1999 ◽  
Vol 112 (3) ◽  
pp. 205-224
Author(s):  
C. Itoh ◽  
T. Minamikawa ◽  
K. Miura ◽  
T. Watanabe
Keyword(s):  
Oscillator Representation ◽  
Energy Eigenvalues ◽  
Representation Method ◽  
Oscillator Representation Method

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.

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.

scholarly journals The problem of a hydrogen atom in a cavity: Oscillator representation solution versus analytic solution

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 61-68
Author(s):  
Sid Chaudhuri
Keyword(s):  
Dielectric Constant ◽  
Spherical Cavity ◽  
Analytic Solution ◽  
Order Approximation ◽  
Energy Levels ◽  
Dielectric Medium ◽  
Cavity Radius ◽  
Oscillator Representation ◽  
Hydrogenic Atom ◽  
Oscillator Representation Method

Abstract A solution to the problem of a hydrogenic atom in a homogeneous dielectric medium with a concentric spherical cavity using the oscillator representation method (ORM) is presented. The results obtained by the ORM are compared with a known exact analytic solution. The energy levels of the hydrogenic atom in a spherical cavity exhibit a shallow-deep instability as a function of the cavity radius. The sharpness of the transition depends on the value of the dielectric constant of the medium. The results of the ORM agree well with the results obtained by the analytic solution when the shallow-deep transition is not too sharp (i.e., when the dielectric constant is not too large) for all values of the cavity radius. The ORM results in the zeroth order approximation diverge significantly in the region of the shallow-deep transition (i.e., for the values of the radius where the shallow-deep transition occurs) when the dielectric constant is high and as a result the transition is sharp. Even for the sharp transition, the ORM results again agree very well with the analytic results at least for the ground state when a commonly used approximation in the ORM is removed. The ORM methodology for the cavity model presented in this article can potentially be used for two-electron systems in a quantum dot.

Calculations of Polarizabilities and Their Gradients for Electron Energy-Loss Spectroscopy

2008 ◽  
Vol 73 (11) ◽  
pp. 1509-1524 ◽  
Author(s):  
Ivana Paidarová ◽  
Roman Čurík ◽  
Stephan P. A. Sauer
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Theoretical Models ◽  
Basis Set ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Perfect Agreement ◽  
Representation Method ◽  
Response Method ◽  
Electron Energy Loss

We illustrate for a set of small hydrocarbons, CH4, C2H4, C3H6 and C3H8, the important role of the electric dipole polarizability tensor and its geometric derivatives in theoretical models of electron energy-loss spectra (EELS). The coupled cluster linear response method together with Sadlej's polarized valence triple zeta basis set of atomic orbitals were used to calculate the polarizabilities and polarizability gradients. Incorporation of these ab initio data into the discrete momentum representation method (DMR) leads to perfect agreement between theory and collision experiments.

scholarly journals Neuronalis összeköttetések a szomatoszenzoros kérgi área 3b és área 1 kézreprezentációs területén főemlősökben

2016 ◽  
Vol 157 (33) ◽  
pp. 1320-1325
Author(s):  
Emese Pálfi ◽  
Mária Ashaber ◽  
Cory Palmer ◽  
Robert M. Friedman ◽  
Anna W. Roe ◽  
...  
Keyword(s):  
Functional Relationship ◽  
Hand Movement ◽  
Saimiri Sciureus ◽  
Skin Area ◽  
Tract Tracing ◽  
Reciprocal Connections ◽  
Representation Method ◽  
Local Input ◽  
Finger Pad ◽  
Area 3B

Introduction: The close functional relationship between areas 3b and 1 of the somatosensory cortex is based on their reciprocal connections indicating that tactile sensation depends on the interaction of these two areas. Aim: The aim of the authors was to explore this neuronal circuit at the level of the distal finger pad representation. Method: The study was made by bidirectional tract tracing aided by neurophysiological mapping in squirrel monkeys (Saimiri sciureus). Results: Inter-areal connections between the two areas preferred the homologues representations. However, intra-areal connections were formed between the neighboring finger pad representations supporting the physiological observations. Interestingly, the size of the local input area of the injected cortical micro-region, which differed in the two areas, represented the same skin area. Conclusions: The authors propose that intra-areal connections are important in integrating information across fingers, while inter-areal connections are important in maintaining input localization during hand movement. Orv. Hetil., 2016, 157(33), 1320–1325.

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