ON THE VARIATIONAL METHOD FOR NONRELATIVISTIC SCATTERING. I. DIFFERENTIAL FORM

Journal Article · Sat Dec 01 04:00:00 EST 1962 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(62)90156-2· OSTI ID:4746174

Malik, F B

Hulthen's (Arkiv f. Mat. Astr. och Fys. 35: No. 25 (1948)) and Kohn's (Phys. Rev., 74: 1783(1948)) sets of equations for the functional of Hulthen are not enough to satisfy the Euler equation of the variational problem (even in case of infinite parameters), which is a necessary condition of the calculus of variation, because the phase shift found in either way usually fails to satisfy the identity obtained from the asymptotic behavior of the wave functions. Since the free boundary condition contains in itself the unknown phase shift, a seif- consistent procedure is invoived. A set of variational equations is suggested where a prescription is given to replace the self-consistency. The prescription ensures that the Schrodinger equation for the scattering comes out as the Euler equation of the variational problem. In this case Hulthen's and Kohn's methods become equivalent. Furthermore, this variational prescription automatically excludes choices of trial wave functions that give rise to varidtional parameters that are discontinuous functions of energy. The importance of the sufficiency condition is stressed. For the specific case of the elastic scattering by He in the Hartree approximation, this prescription gives better results than Hulthen's or Kohn's method. (auth)

• Research Organization: Princeton Univ., N.J.; Fordham Univ., New York; and Pakistan Atomic Energy Commission, Karachi
• NSA Number: NSA-17-007507
• OSTI ID: 4746174
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 20; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

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