Determination of closed expressions for the perturbation theory corrections to the wave functions of bound states by means of a Sturm function expansion

1974 ◽  
Vol 21 (2) ◽  
pp. 1097-1104 ◽  
Author(s):  
A. I. Sherstyuk
Keyword(s):  
Perturbation Theory ◽  
Bound States ◽  
Wave Functions ◽  
Function Expansion

scholarly journals SCHRÖDINGER EQUATION FOR HEAVY MESONS EXPANDED IN 1/mQ

1996 ◽  
Vol 11 (03) ◽  
pp. 257-266 ◽  
Author(s):  
TAKAYUKI MATSUKI
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Higher Order ◽  
Wave Functions ◽  
Heavy Mesons ◽  
Higher Order Corrections

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schrödinger equation for [Formula: see text] bound states described by a Hamiltonian, we systematically develop a perturbation theory in 1/mQ which enables one to solve the Schrödinger equation to obtain masses and wave functions of the bound states in any order of 1/mQ. There also appear negative components of the wave function in our formulation which contribute also to higher order corrections to masses.

scholarly journals Trapping electrons in a circular graphene quantum dot with Gaussian potential

2018 ◽  
Vol 28 (1) ◽  
pp. 51
Author(s):  
Nhung T. T. Nguyen
Keyword(s):  
Angular Momentum ◽  
Quantum Dot ◽  
Bound States ◽  
Effective Radius ◽  
Wave Functions ◽  
Graphene Quantum Dot ◽  
Trapping Time ◽  
Gaussian Potential ◽  
Weyl Equation

We study the dependence of trapping time of an electron in a circular graphene quantum dot depends on the electron's angular momentum and on the parameters of the external Gaussian potential used to induce the dot. The trapping times are calculated through a numerical determination of the quasi-bound states of electron from the two-dimensional Dirac-Weyl equation. It is shown that on increasing the angular momentum, not only does the trapping time decreases but also the trend of how the trapping time depends on the effective radius of the dot changes. In particular, as the dot radius increases, the trapping time increases for m<3 but decreases for m > 3. The trapping time however always decreases upon increasing the potential height. It is also found that the wave functions corresponding to the states of larger trapping times or higher m are more localized in space.

scholarly journals Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

Wave functions for weakly coupled bound states

1982 ◽  
Vol 25 (5) ◽  
pp. 2467-2472 ◽  
Author(s):  
S. H. Patil
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Weakly Coupled

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

Applicability of the schrödinger perturbation theory to bound states

1964 ◽  
Vol 10 (1) ◽  
pp. 73 ◽  
Author(s):  
K. Hausmann ◽  
W. Macke ◽  
P. Ziesche
Keyword(s):  
Perturbation Theory ◽  
Bound States ◽  
Schrödinger Perturbation

scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

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