Analytical expressions for the energies of anharmonic oscillators

2000 ◽  
Vol 78 (9) ◽  
pp. 845-850
Author(s):  
F M Fernández ◽  
R H Tipping
Keyword(s):  
Perturbation Parameter ◽  
Bound State ◽  
Perturbation Series ◽  
Simple Expression ◽  
Branch Points ◽  
Anharmonic Oscillators ◽  
Large Coupling ◽  
Analytical Behavior ◽  
Schrödinger Perturbation ◽  
Analytical Expressions

We propose a systematic construction of algebraic approximants for the bound-state energies of anharmonic oscillators. The approximants are based on the Rayleigh-Schrödinger perturbation series and take into account the analytical behavior of the energies at large values of the perturbation parameter. A simple expression obtained from a low-order perturbation series compares favorably with alternative approximants. Present approximants converge in the large-coupling limit and are suitable for the calculation of the energy of highly excited states. Moreover, we obtain some branch points of the eigenvalues of the anharmonic oscillator as functions of the coupling constant. PACS No.: 03.65Ge

Linear bounded potential model for semiconductor band bending

2022 ◽  
Author(s):  
Facundo Villavicencio ◽  
Jorge Mario Ferreyra ◽  
German Bridoux ◽  
Manuel Villafuerte
Keyword(s):  
Potential Model ◽  
Simple Expression ◽  
Linear Potential ◽  
Charge Balance ◽  
Band Bending ◽  
Mass Approximation ◽  
Hole Confinement ◽  
Dimensional Electron Gas ◽  
Analytical Expressions ◽  
Franz Keldysh Effect

Abstract We propose a simple but unexplored model for the semiconductor band bending with the aim to obtain a relatively simple expression to calculate the energy spectrum for the confined levels and the analytical expressions for wave-functions. This model consists of a linear potential but it is bounded or trimmed in energy unlike the well known wedge potential model. We present exact solutions for this potential in the frame of the effective mass approximation and they are valid for electron or hole confinement potential. This model provides a more adequate physical scenario than the wedge potential since it takes into account the charge balance involved in the band bending potential. These results allow to treat confined potential problems as in the case of a two-dimensional electron gas (2DEG) in a simplified way. We discuss the application of this approximation to the recombination time of electrons an holes and for the Franz-Keldysh effect.

scholarly journals Molecular-Theory of High Frequency Dielectric Susceptibility of Nematic Nanocomposites

Crystals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 970
Author(s):  
Mikhail A. Osipov ◽  
Alexey S. Merekalov ◽  
Alexander A. Ezhov
Keyword(s):  
Plasmon Resonance ◽  
High Frequency ◽  
Volume Fraction ◽  
Simple Expression ◽  
Dielectric Anisotropy ◽  
Dielectric Susceptibility ◽  
Nanoparticle Volume Fraction ◽  
Effective Polarizability ◽  
Dielectric And Optical Properties ◽  
Analytical Expressions

A molecular-statistical theory of the high frequency dielectric susceptibility of the nematic nanocomposites has been developed and approximate analytical expressions for the susceptibility have been obtained in terms of the effective polarizability of a nanoparticle in the nematic host, volume fraction of the nanoparticles and the susceptibility of the pure nematic phase. A simple expression for the split of the plasmon resonance of the nanoparticles in the nematic host has been obtained and it has been shown that in the resonance frequency range the high frequency dielectric anisotropy of the nanocomposite may be significantly larger than that of the pure nematic host. As a result, all dielectric and optical properties of the nanocomposite related to the anisotropy are significantly enhanced which may be important for emerging applications. The components of the dielectric susceptibility have been calculated numerically for particular nematic nanocomposites with gold and silver nanoparicles as functions of the nanoparticle volume fraction and frequency. The splitting of the plasmon resonance has been observed together with the significant dependence on the nanoparticle volume fraction and the parameters of the nematic host phase.

scholarly journals Motions of the String Solutions in the XXZ Spin Chain Under a Varying Twist

1997 ◽  
Vol 12 (04) ◽  
pp. 801-838 ◽  
Author(s):  
N. Fumita ◽  
H. Itoyama ◽  
T. Oota
Keyword(s):  
Ground State ◽  
Spin Chain ◽  
Imaginary Axis ◽  
Berry Phase ◽  
Numerical Study ◽  
Twist Angle ◽  
Finite Size ◽  
Bound State ◽  
Branch Points ◽  
Finite Size Corrections

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study in a finite size system. In the attractive critical regime 0 < Δ < 1, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of n-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase in the regime Δ ≤ -1 also, establishing the continuity of the previous results at -1 < Δ < 0 to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle (or the bound state) involved in the process.

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