On a canonical functions approach to the elastic scattering phase-shift problem

1991 ◽  
Vol 40 (1) ◽  
pp. 11-21 ◽  
Author(s):  
Hafez Kobeissi ◽  
Khaled Fakhreddine ◽  
Majida Kobeissi
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Shift Problem ◽  
Scattering Phase

High-algebraic, high-phase lag methods for accurate computations for the elastic- scattering phase shift problem

1998 ◽  
Vol 76 (6) ◽  
pp. 473-493 ◽  
Author(s):  
T E Simos
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Finite Difference Methods ◽  
Phase Lag ◽  
New Methods ◽  
Shift Problem ◽  
Algebraic Order ◽  
Scattering Phase

A family of three new hybrid eighth-algebraic-order two-step methods with phase lag of order 16, 18, and 20 are developed for computing elastic-scattering phase shifts of the one-dimensional Schrödinger equation. Based on these new methods, we obtain some new embedded variable-step procedures for the numerical integration of the Schrödinger equation. Numerical results obtained for both the integration of the phase-shift problem for the well known case of the Lennard–Jones potential and the integration of coupled differential equation arising from the Schrödinger equation show that these new methods are better than other finite-difference methods. PACS Nos.: 02.00, 02.70, 03.00, 03.65

AN EIGHTH-ORDER METHOD WITH MINIMAL PHASE-LAG FOR ACCURATE COMPUTATIONS FOR THE ELASTIC SCATTERING PHASE-SHIFT PROBLEM

1996 ◽  
Vol 07 (06) ◽  
pp. 825-835 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Finite Difference Methods ◽  
New Method ◽  
Phase Lag ◽  
Step Method ◽  
Shift Problem ◽  
Scattering Phase

A new hybrid eighth-algebraic-order two-step method with phase-lag of order ten is developed for computing elastic scattering phase shifts of the one-dimensional Schrödinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lenard–Jones potential show that this new method is better than other finite difference methods.

AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2005 ◽  
Vol 16 (06) ◽  
pp. 879-894 ◽  
Author(s):  
HANS VAN DE VYVER
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Coupled Differential Equations ◽  
Shift Problem ◽  
Scattering Phase ◽  
Runge Kutta

A new way for constructing efficient embedded modified Runge–Kutta methods for the numerical solution of the Schrödinger equation is presented in this paper. The methods of the embedded scheme have algebraic orders five and four. Applications of the new pair to the elastic scattering phase-shift problem and coupled differential equations of Schrödinger type indicate that the new pair is much more efficient than other well known comparable embedded Runge–Kutta pairs.

K+p interactions in the range 0.9–1.5 GeV/c and elastic scattering phase shift analysis

1970 ◽  
Vol 20 (2) ◽  
pp. 301-319 ◽  
Author(s):  
G. Giacomelli ◽  
P. Lugaresi-Serra ◽  
G. Mandrioli ◽  
A.M. Rossi ◽  
F. Griffiths ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Phase Shift Analysis ◽  
Shift Analysis ◽  
Scattering Phase

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

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