The Scattering Amplitude for the Schrödinger Equation with a Long-Range Potential

1998 ◽  
Vol 191 (1) ◽  
pp. 183-218 ◽  
Author(s):  
D. Yafaev
Keyword(s):  
Schrödinger Equation ◽  
Long Range ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Range Potential

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Gao-Feng Wei ◽  
Wen-Chao Qiang ◽  
Wen-Li Chen
Keyword(s):  
Schrödinger Equation ◽  
Diatomic Molecule ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Energy Levels ◽  
Bound State ◽  
Radial Wave ◽  
Continuous States ◽  
Analytical Properties ◽  
Function Potential

AbstractThe continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.

scholarly journals A NOTE ON COULOMB SCATTERING AMPLITUDE

2007 ◽  
Vol 22 (18) ◽  
pp. 3131-3136
Author(s):  
ZAFAR AHMED
Keyword(s):  
Schrödinger Equation ◽  
Partial Wave ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Coulomb Scattering ◽  
Cylindrical Coordinates ◽  
General Method

The summation of the partial wave series for Coulomb scattering amplitude, fC(θ) is usually avoided because the series is oscillatorily and divergent. Instead, fC(θ) is generally obtained by solving the Schrödinger equation in parabolic cylindrical coordinates which is not a general method. Here, we show that a reconstructed series, (1- cos θ)2fC(θ), is both convergent and analytically summable.

scholarly journals On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions

2001 ◽  
Vol 6 (6) ◽  
pp. 329-338
Author(s):  
Yuriy Valentinovich Zasorin
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Explicit Form ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Wave Functions ◽  
Stationary Schrödinger Equation ◽  
Fixed Level

For stationary Schrödinger equation inℝ nwith the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.

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