Spinless Salpeter equation: Laguerre bounds on energy levels
نویسندگان
چکیده
منابع مشابه
Spinless Salpeter Equation: Laguerre Bounds on Energy Levels
The spinless Salpeter equation may be considered either as a standard approximation to the Bethe–Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the costumary nonrelativistic Schrödinger formalism. Because of the presence of the rather difficult-to-handle square...
متن کاملEnergy Bounds for the Spinless Salpeter Equation
We study the spectrum of the Salpeter Hamiltonian H = β √ m2 + p2 +V (r), where V (r) is an attractive central potential in three dimensions. If V (r) is a convex transformation of the Coulomb potential −1/r and a concave transformation of the harmonic-oscillator potential r, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form ...
متن کاملEnergy 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 کاملLower Bounds for the Spinless Salpeter Equation
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.
متن کاملSpinless 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review A
سال: 1997
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.56.139