Abstract The intention of this paper is to determine some of the properties of the screened coulomb [sic] potential, and look into its validity as a model for observed emission spectra of hydrogen plasmas. Some variational methods will be examined and the problem of finding upper bounds to the excited states of atoms will also be investigated. The variational method is then applied to the anomoly [sic] of the...

Abstract A survey of the relative efficiency of various approximate methods for solving the non-relativistic Schroedinger Equation [sic] is made. In particular, a comparison is made of the results obtained for the problem of a simple harmonic oscillator perturbed by λx∝, (∝ =3,4 ) while using the Rayleigh-Ritz variational principle, Linear Variation of Functions, and the Reyleigh-Schroedinger [sic]...

Abstract In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form λx∝ are studied were λ is the coupling constant. The method is demonstrated by a general derviation of the wavefunctions to third order for any ∝ and quantum number n. Additonal expressions are presented for the ground states to tenth order in the energy. It is also shown that the "matching condition" for the basic and...

Abstract The Schrodinger equation for an atomic system which possesses N electrons has 3N independent variables and is perhaps one of the most difficult questions in physics to solve. Because of the complex nature of the problem, only approximate methods can be used. One such method is the Rayleigh-Ritz Variational principle [sic] which minmizes over all [sic] space, and the minimum is the ground state energy. Another method is by...

Abstract The non-relativistic energies have been determined for the singlet and triple S states (1¹S, 2¹S and 2³S) of the helium like two electron system. Calculations were based on a finite set of orbitals of the order 7. The set, which includes Laguerre polynomials, is expressed as a superposition of configurations built up from one-electron wave functions or orbitals and approximates the exact wave function. Application of the variational principle leads to a system of linear equations....