6,531 research outputs found

    Upper limit on the critical strength of central potentials in relativistic quantum mechanics

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    In the context of relativistic quantum mechanics, where the Schr\"odinger equation is replaced by the spinless Salpeter equation, we show how to construct a large class of upper limits on the critical value, gc(ℓ)g_{\rm{c}}^{(\ell)}, of the coupling constant, gg, of the central potential, V(r)=−gv(r)V(r)=-g v(r). This critical value is the value of gg for which a first ℓ\ell-wave bound state appears.Comment: 8 page

    Comment on `Glueball spectrum from a potential model'

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    In a recent article, W.-S. Hou and G.-G. Wong [Phys. Rev. D {\bf 67}, 034003 (2003)] have investigated the spectrum of two-gluon glueballs below 3 GeV in a potential model with a dynamical gluon mass. We point out that, among the 18 states calculated by the authors, only three are physical. The other states either are spurious or possess a finite mass only due to an arbitrary restriction of the variational parameter.Comment: Comment on pape

    A semiclassical model of light mesons

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    The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of two different finite quark masses and potential parameters on Regge and vibrational trajectories is discussed.Comment: 1 figur

    Sufficient conditions for the existence of bound states in a central potential

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    We show how a large class of sufficient conditions for the existence of bound states, in non-positive central potentials, can be constructed. These sufficient conditions yield upper limits on the critical value, gc(ℓ)g_{\rm{c}}^{(\ell)}, of the coupling constant (strength), gg, of the potential, V(r)=−gv(r)V(r)=-g v(r), for which a first ℓ\ell-wave bound state appears. These upper limits are significantly more stringent than hitherto known results.Comment: 7 page

    Electromagnetic splitting for mesons and baryons using dressed constituent quarks

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    Electromagnetic splittings for mesons and baryons are calculated in a formalism where the constituent quarks are considered as dressed quasiparticles. The electromagnetic interaction, which contains coulomb, contact, and hyperfine terms, is folded with the quark electrical density. Two different types of strong potentials are considered. Numerical treatment is done very carefully and several approximations are discussed in detail. Our model contains only one free parameter and the agreement with experimental data is reasonable although it seems very difficult to obtain a perfect description in any case.Comment: 14 pages, Revised published versio

    Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials

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    The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schr\"{o}dinger equation with exponential potentials of the form −αrλexp⁥(−ÎČr)-\alpha r^\lambda \exp(-\beta r) can also be analytically solved by using the auxiliary field method. Formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn on the Yukawa potential and the pure exponential one

    On the modification of Hamiltonians' spectrum in gravitational quantum mechanics

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    Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies the Heisenberg uncertainty principle. This modified version is usually called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes all Hamiltonians in quantum mechanics. In this Letter, we use a recently proposed GUP which is consistent with String Theory, Doubly Special Relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. This form of GUP results in two additional terms in any quantum mechanical Hamiltonian, proportional to αp3\alpha p^3 and α2p4\alpha^2 p^4, respectively, where α∌1/MPlc\alpha \sim 1/M_{Pl}c is the GUP parameter. By considering both terms as perturbations, we study two quantum mechanical systems in the framework of the proposed GUP: a particle in a box and a simple harmonic oscillator. We demonstrate that, for the general polynomial potentials, the corrections to the highly excited eigenenergies are proportional to their square values. We show that this result is exact for the case of a particle in a box.Comment: 11 pages, to appear in Europhysics Letter

    Comment on "Quantum mechanics of smeared particles"

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    In a recent article, Sastry has proposed a quantum mechanics of smeared particles. We show that the effects induced by the modification of the Heisenberg algebra, proposed to take into account the delocalization of a particle defined via its Compton wavelength, are important enough to be excluded experimentally.Comment: 2 page

    Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states

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    In the context of non-relativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed by two-body bound by a central potential. A lower limit on the mean square radius is used to obtain a simple criteria for the occurrence of S-wave quantum halo sates.Comment: 12 pages, 2 figure

    Renormalization of the singular attractive 1/r41/r^4 potential

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    We study the radial Schr\"odinger equation for a particle of mass mm in the field of a singular attractive g2/r4g^2/{r^4} potential with particular emphasis on the bound states problem. Using the regularization method of Beane \textit{et al.}, we solve analytically the corresponding ``renormalization group flow" equation. We find in agreement with previous studies that its solution exhibits a limit cycle behavior and has infinitely many branches. We show that a continuous choice for the solution corresponds to a given fixed number of bound states and to low energy phase shifts that vary continuously with energy. We study in detail the connection between this regularization method and a conventional method modifying the short range part of the potential with an infinitely repulsive hard core. We show that both methods yield bound states results in close agreement even though the regularization method of Beane \textit{et al.} does not include explicitly any new scale in the problem. We further illustrate the use of the regularization method in the computation of electron bound states in the field of neutral polarizable molecules without dipole moment. We find the binding energy of s-wave polarization bound electrons in the field of C60_{60} molecules to be 17 meV for a scattering length corresponding to a hard core radius of the size of the molecule radius (∌3.37\sim 3.37 \AA). This result can be further compared with recent two-parameter fits using the Lennard-Jones potential yielding binding energies ranging from 3 to 25 meV.Comment: 8 page
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