共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Nenciu 《Communications in Mathematical Physics》1976,48(3):235-247
Some general results about perturbations of not-semibounded self-adjoint operators by quadratic forms are obtained. These are applied to obtain the distinguished self-adjoint extension for Dirac operators with singular potentials (including potentials dominated by the Coulomb potential withZ<137). The distinguished self-adjoint extension, is theunique self-adjoint extension, for which the wave functions in its domain possess finite mean kinetic energy. It is shown moreover that the essential spectrum of the distinguished extension is contained in the spectrum of the free Hamiltonian. 相似文献
2.
A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of
the effective potentials deduced under the
algebra can be brought back to the general Natanzon hypergeometric potentials. 相似文献
3.
We derive an effectiveN-N potential from a microscopic quark Hamiltonian using the quark cluster model. We construct it in an explicit analytical form, which is expressed only by nuclear variables and which can be used in nuclear structure calculations. To this end we first solve the equation of motion for the six-quark system with a microscopic quark Hamiltonian that includes the quadratic-confinement, one-gluon-, and one-pion-exchange potentials. We then eliminate the quark (internal) degrees of freedom explicitly and express them implicitly in terms of an effectiveN-N potential. The equation of motion for the two-nucleon system is then described by a Schrödinger equation with an effectiveN-N potential. In addition to the one-pion-exchange potential, this effectiveN-N potential contains thequark-exchange potential, which represents the quark-exchange processes associated with a gluon or a pion exchange. This quark-exchange potential is incorporated into the effectiveN-N potential through nonlocal and isospin-dependent terms, which produce a short-range repulsion in theN-N interaction. We give the explicit analytical form of this quark-exchange potential so that it can be used in the nuclear structure calculations.Supported by the DFG under contract number Fa 67/10-5Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday 相似文献
4.
H. Leeb H. Fiedeldey E. J. O. Gavin S. A. Sofianos R. Lipperheide 《Few-Body Systems》1992,12(2-4):55-68
We show that it is in principle possible to determine the quark-quark potential, in the nonrelativistic potential model, from the baryon spectrum. The method we propose is based on the fact that the lowest order of the hyperspherical-harmonic expansion method, the hypercentral approximation, is an excellent approximation for confining quark-quark potentials. However, our method applies to all cases where this assumption is valid. Using standard inverse spectrum techniques adapted to our problem we invert the baryon spectrum to obtain the hypercentral potential in the hyperradius of the three-quark system. By means of a new exact relation based on the Abel integral equation, we can invert the hypercentral potential to determine the quark-quark potential.A first application of this new method to the inversion of thes-state baryon spectrum demonstrates in a model-independent way the inability of nonrelativistic two-quark potentials to reproduce the Roper resonance without violating the QCD-motivated concavity requirement.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays 相似文献
5.
Fernando Izaurieta Eduardo Rodríguez Patricio Salgado 《Letters in Mathematical Physics》2007,80(2):127-138
In the context of Chern–Simons (CS) Theory, a subspace separation method for the Lagrangian is proposed. The method is based on the iterative use of the Extended Cartan Homotopy Formula, and allows
one to (1) separate the action in bulk and boundary contributions, and (2) systematically split the Lagrangian in appropriate
reflection of the subspace structure of the gauge algebra. In order to apply the method, one must regard CS forms as a particular
case of more general objects known as transgression forms. Five-dimensional CS Supergravity is used as an example to illustrate the method.
相似文献
6.
Maurizio De Sanctis 《Central European Journal of Physics》2014,12(4):221-232
We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame. A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data. 相似文献
7.
Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq
3 = 1 and the particularq
4 = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively. 相似文献
8.
Doron Gepner 《Communications in Mathematical Physics》1991,141(2):381-411
The algebraic structure of fusion rings in rational conformal field theories is analyzed in detail in this paper. A formalism which closely parallels classical tools in the study of the cohomology of homogeneous spaces is developed for fusion rings, in general, and for current algebra theories, in particular. It is shown that fusion rings lead to a natural orthogonal polynomial structure. The rings are expressed through generators and relations. The relations are then derived from some potentials leading to an identification of the fusion rings with deformations of affine varieties. In general, the fusion algebras are mapped to affine varieties which are the locus of the relations. The connection with modular transformations is investigated in this picture. It is explained how chiral algebras, arising inN=2 superconformal field theory, can be derived from fusion rings. In particular, it is argued that theories of the typeSU(N)
k
/SU(n–1) are theN=2 counterparts of Grassmann manifolds and that there is a natural identification of the chiral fields with Schubert varieties, which is a graded algebra isomorphism.Supported in part by NSF grant PHY 89-04035 supplemented by funds from NASA 相似文献
9.
In a one-dimensional quantal solution of Schroedinger equation, the general expressions for reflection and transmission coefficients
are derived for a potential constituting n number of rectangular wells and barriers. These expressions are readily used for the estimation of eigenvalues of a smooth
potential which is simulated by a multi-step potential. The applicability of this method is demonstrated with success in potentials
with different forms including the most versatile Ginocchio potential where the widely used numerical method like Runge-Kutta
integration algorithm fails to yield the result. Accurate evaluation of eigenvalues free from numerical problem for any form
of potentials, whether analytically solvable or not, is the highlight of the present multi-step approximation method in the
theory of potential scattering.
相似文献
10.
We find that a single two-variable integro-differential equation, which includes all two-body correlations, produces results for three- and four-body bound systems in good agreement with those obtained with the most accurate methods and also that for sixteen fermions, interacting by means of local Wigner-type potentials our results agree with those obtained with the Variational Monte-Carlo and the Fermi-Hypernetted chain methods.This equation includes a hypercentral potential. When it is set equal to zero it reduces to theS-state projected potential version of the formalism, which for three nucleons is identical to the exact Faddeev equation forS-state projected potentials.We show that the inclusion of the hypercentral component of the two-body local potential, which operates on all orbitals, takes the effect of the higher partial waves largely into account without the need of solving a system of coupled integro-differential equations. We, furthermore, show that by using the Weight-Function Approximation our integro-differential equation is transformed into a simple inhomogeneous differential equation, which becomes accurate forA16.The major advantages of our approximate method are, firstly, that unlike the exact Faddeev-Yakubovsky and Alt-Grassberger-Sandhas equations or the Monte-Carlo methods, it does not become rapidly unmanageable, but even simplifies with increasingA and, secondly, the speed and simplicity of our numerical calculations. 相似文献
11.
SU(2) andSU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
Constantin Brif 《International Journal of Theoretical Physics》1997,36(7):1651-1682
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of
the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated
with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent
states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset
of algebra eigenstates. We develop the general formalism and apply it to theSU(2) andSU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in both cases by a method that employs
analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions
for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states
and intelligent states are examined and relations between them are studied by using their analytic representations. 相似文献
12.
The spectrum of r ?1 and r ?2 type potentials of diatomic molecules in radial Schrödinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the α, β, γ and σ parameters. 相似文献
13.
Bohr–Mottelson Hamiltonian on the γ-rigid regime for Q-deformed modified Eckart and three-dimensional harmonic oscillator potentials in the β-collective shape variable was investigated in the presence of minimal length formalism and Q-deformed of the radial momentum part. By introducing new wave function and using the Q-deformed potential concept in Bohr–Mottelson Hamiltonian in the minimal length formalism, the un-normalized wave function and energy spectra equation were obtained by using the hypergeometric method. Meanwhile, the Bohr–Mottelson Hamiltonian in the presence of the quadratic spatial deformation to the momentum in collective shape variable was investigated using transformation of a new variable such as the Schrodinger-like equation with shape invariant potential. The energy equation and un-normalized wave function were obtained using the hypergeometric method. The results showed that the Bohr–Mottelson equations with different energy potentials and different deformation forms in the radial momentum reduced to the similar Schrodinger-like equation with the modified Poschl–Teller potential. 相似文献
14.
O. Ogievetsky W. B. Schmidke J. Wess B. Zumino 《Communications in Mathematical Physics》1992,150(3):495-518
Theq-differential calculus for theq-Minkowski space is developed. The algebra of theq-derivatives with theq-Lorentz generators is found giving theq-deformation of the Poincaré algebra. The reality structure of theq-Poincaré algebra is given. The reality structure of theq-differentials is also found. The real Laplacian is constructed. Finally the comultiplication, counit and antipode for theq-Poincaré algebra are obtained making it a Hopf algebra.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139 相似文献
15.
We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate
(4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential
or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator.
We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable
system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials. 相似文献
16.
A. V. Matveenko 《Few-Body Systems》1988,4(2):103-109
Recently we proposed an exact transformation of the three-body Schrödinger operator in the form usually applied in the Born-Oppenheimer method. This transformation removed all the shortcomings of the Born-Oppenheimer method associated with an incorrect behaviour of an approximate solution in the regions of pair and triple collisions. In the present paper the relation of the new method with the adiabatic hyperspherical approach, which was successfully applied to study the He atom and theeee
+ ion, is pointed out. The weakly bound state of thedt
– ion is used as an example to demonstrate the advantages of the new approach in calculating also molecular systems. It is argued that the proposed method, which represents a natural combination of the two well-known approaches, is well applicable to solve a wide spectrum of fewbody problems. 相似文献
17.
Whenq is a root of unity, the representations of the quantum universal enveloping algebra sl
q
(2) with multiplicity two are constructed from theq-deformed boson realization with an arbitrary parameter which is in a very general form and is first presented in this Letter. The new solutions to the Yang-Baxter equation are obtained from these representations through the universalR-matrix.This work is supported in part by the National Foundation of Natural Science of China. 相似文献
18.
By means of the linear quantum transformation (LQT) theory, a concisediagonalization approach for then-mode boson quadratic Hamiltonian is given,and a general method to calculate the wave function is proposed. 相似文献
19.
In this paper, the Lie symmetry algebra of the coupled
Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and
this algebra is shown to have
a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP
equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the
general symmetry groups, the Lie symmetry group can be recovered and a group
of discrete transformations can be derived simultaneously. Lastly,
from a known simple solution of the cKP equation, we can easily obtain
two new solutions by the general symmetry groups. 相似文献
20.
R. Coquereaux L. Frappat E. Ragoucy P. Sorba 《Communications in Mathematical Physics》1990,133(1):1-35
We study theN-extended super-Ka-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleA
N
. The extensions are characterized by 2-cocycles which are computed in terms of the cyclic cohomology of the Grassmann algebra withN generators. The graded algebra of super-derivations compatible with each extension is determined. The casesN=1,2,3 are examined in detail and their relation with the Ademollo et al. superconformal algebras is discussed. We examine the possibility of defining new superconformal algebras which, forN>1, generalize theN=1 Ramond-Neveu-Schwarz algebra. 相似文献