Energy Bounds for the Spinless Salpeter Equation
نویسندگان
چکیده
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 E = min r>0 β √ m2 + P 2 r2 + V (r) for suitable values of P here provided. At the critical point r = r̂ the relative growth to the Coulomb potential h(r) = −1/r must be bounded by dV/dh < 2β/π. PACS numbers : 03.65.Ge, 03.65.Pm, 11.10.St ‡ E-mail address : [email protected] ∗ E-mail address : [email protected] † E-mail address : [email protected]
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