A trial wavefunction, Psi 1 , which contains both linear and nonlinear parameters is constructed using an approximate target wavefunction, Psi 1 is related to a quantity, a v , which becomes the Kohn scattering length if the target wavefunction is exact, through an integral expression corresponding to a slight modification of the usual Kohn variational method. It is conjectured that if the values of a v display a local minimum when all the nonlinear parameters of Psi 1 are varied, then this local minimum value of a v is an upper bound on the exact scattering length. Calculations on the zero-energy positron-helium scattering system using Hylleraas-type approximations to the helium ground-state wavefunction are analysed using this criterion. The use of either a six-parameter or a ten-parameter Hylleraas-type approximation to the helium ground-state wavefunction can give good results in scattering calculations for the positron-helium system at zero energy.A trial wavefunction, Psi 1 , which contains both linear and nonlinear parameters is constructed using an approximate target wavefunction, Psi 1 is related to a quantity, a v , which becomes the Kohn scattering length if the target wavefunction is exact, through an integral expression corresponding to a slight modification of the usual Kohn variational method. It is conjectured that if the values of a v display a local minimum when all the nonlinear parameters of Psi 1 are varied, then this local minimum value of a v is an upper bound on the exact scattering length. Calculations on the zero-energy positron-helium scattering system using Hylleraas-type approximations to the helium ground-state wavefunction are analysed using this criterion. The use of either a six-parameter or a ten-parameter Hylleraas-type approximation to the helium ground-state wavefunction can give good results in scattering calculations for the positron-helium system at zero energy.

Journal of Physics B Atomic and Molecular PhysicsOct 21, 197516 citations

An experiment regarding the wave function of superfluid helium

Marvin Chester, E. Guyon, Brian K. Jones

Solid State CommunicationsOct 1, 19671 citation

An Anti-WKB Approximation

John B. Bronzan

In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $ϕ^4$ field theory.In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $ϕ^4$ field theory.

arXiv:hep-ph/9503225Mar 3, 19950 citations

Tests of Macroscopic Wave Function Theories of Helium II

Andrew A. Moulthrop

Jan 1, 19840 citations

In the WKB approximation the

\nabla^2S

term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the

\nabla^2 S

term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to

ϕ^4

field theory.