Lower Bounds for the Spinless Salpeter Equation

نویسندگان

  • Fabian BRAU
  • Francesco Calogero
  • F Brau
چکیده

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schrödinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in L(R) for some p > n (n = 1 or 3). An extension to confining potentials, which are not in L(R), is also presented.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

THE SPINLESS SALPETER EQUATION AND MESON DYNAMICS

Applying the variational method, the spinless reduced Bethe-Salpeter (RBS) equation is solved for the mesonic systems, and the mass spectra are obtained. The method is applied to the Hamiltonian with the Gaussian and hydrogen-type trial wave functions, and different potential models are examined. The results for the different potentials are in challenge in light mesons, while they are consisten...

متن کامل

Energy Bounds for the Spinless Salpeter Equation: Harmonic Oscillator

We study the eigenvalues En` of the Salpeter Hamiltonian H = β √ m2 + p2 +vr, v > 0, β > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula En` ≈ min r>0 { v(Pn`/r) 2 + β √ m2 + r2 } provides both upper and lower energy bounds for all the eigenvalues of the problem. PACS: 03.65.Ge, 03.65.Pm, 11.10.St En...

متن کامل

Spinless Salpeter Equation: Analytic Results

The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic statements on resulting solutions. In view of this unsatisfactory state of affairs, we calculate analytic upper bounds on the involved energy levels, and, for th...

متن کامل

Integral equation formulation of the spinless Salpeter equation

The spinless Salpeter equation presents a rather particular differential operator. In this paper we rewrite this equation into integral and integro-differential equations. This kind of equations are well known and can be more easily handled. We also present some analytical results concerning the spinless Salpeter equation and the action of the square-root operator. 03.65.Pm, 02.30.Rz Typeset us...

متن کامل

The One-dimensional Spinless Relativistic Coulomb Problem

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a (“hard-core amended”) Coulomb interaction potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues....

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004