A method of computing phase shifts and normalizations of continuum-state dirac wave functions

1962 ◽  
Vol 25 (5) ◽  
pp. 1061-1071 ◽  
Author(s):  
I. Hauser ◽  
R. J. Malhiot
Keyword(s):  
Phase Shifts ◽  
Wave Functions ◽  
Continuum State

scholarly journals THE LORENTZ INTEGRAL TRANSFORM (LIT) METHOD

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1339-1358 ◽  
Author(s):  
WINFRIED LEIDEMANN
Keyword(s):  
Ab Initio Calculations ◽  
Integral Transform ◽  
Bound State ◽  
Particle Systems ◽  
Wave Functions ◽  
Many Body ◽  
State Problem ◽  
Continuum State ◽  
Lorentz Integral Transform ◽  
Continuum Wave

The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT approach opens up the possibility to perform ab initio calculations of reactions also for those particle systems which presently are out of reach in conventional approaches with explicit calculations of many-body continuum wave functions. Various LIT applications are discussed ranging from particle systems with two nucleons up to particle systems with seven nucleons.

Correction for the Uniform WKB Wave Functions and the WKB Phase Shifts

1974 ◽  
Vol 52 (18) ◽  
pp. 1805-1815 ◽  
Author(s):  
Byung Chan Eu ◽  
Hervé G. Guerin
Keyword(s):  
Numerical Solution ◽  
Present Method ◽  
Turning Point ◽  
Numerical Test ◽  
Equation Of Motion ◽  
Phase Shifts ◽  
Wave Functions ◽  
Wkb Approximation ◽  
Wkb Method ◽  
Connection Formulas

A method of improving the uniform WKB solution for single turning point problems is discussed and the correction formulas for the WKB phase shifts are obtained. The method involves the equation of motion which is in a form similar to that used by Fröman and Fröman to obtain the connection formulas in the WKB approximation. A sequence of solutions to the equation of motion is obtained in a remarkably compact form—and in a novel way—by utilizing the involutionality of certain 2 × 2 matrices appearing in the equations. A numerical test of the result thus obtained is presented in comparison with the corresponding numerical solution result. Unlike the ordinary WKB method, the present method is completely free of the connection formulas of the WKB approximation.

The Filterization Method to Calculate Eigenstates

1997 ◽  
Vol 11 (03) ◽  
pp. 295-302
Author(s):  
Fahrettin Gögtas ◽  
A. Kadir Yildiz ◽  
Gabriel G. Balint-Kurti
Keyword(s):  
Wave Function ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Grid Method ◽  
Hamiltonian Operator ◽  
Bound State ◽  
Wave Functions ◽  
Continuum State ◽  
Triatomic Molecules

We have proposed a new method to calculate low lying eigenstates of Hamiltonian operator for triatomic molecules. The method is a grid method based on continuously pumping flux onto the potential energy surface and gives the wave function overlapping with prechosen energy of interest. This energy may correspond to a bound state, a resonance or a continuum state. We have calculated several low lying bound state energies and corresponding bound state wave functions for HOCl with HO bond fixed at its equilibrium value.

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