General asymptotic form of wave function for system of charged particles

1977 ◽  
Vol 62 (2) ◽  
pp. 81-82 ◽  
Author(s):  
R. Peterkop
Keyword(s):  
Wave Function ◽  
Asymptotic Form ◽  
Charged Particles

Quantization of a Free Particle in a Dissipative Medium: Interaction of Charged Particles With Matter

2005 ◽  
Author(s):  
Eqab M. Rabei ◽  
Abdul-Wali Ajlouni ◽  
Humam B. Ghassib
Keyword(s):  
Wave Function ◽  
Energy Loss ◽  
Free Particle ◽  
Canonical Quantization ◽  
Charged Particles ◽  
Dissipative Medium ◽  
Nonconservative Systems ◽  
Damping Effect ◽  
Free Particles ◽  
Set Up

Following our work on the quantization of nonconservative systems using fractional calculus, the canonical quantization of a system of free particles in a dissipative medium is carried out according to the Dirac method. A suitable Schro¨dinger equation is set up and solved for the Lagrangian representing this system. The wave function is plotted and the damping effect manifests itself very clearly. This formalism is then applied to the problem of energy loss of charged particles when passing through matter. The results are plotted and the relation between the energy loss and the range agrees qualitatively with experimental results.

Asymptotic wave function for three charged particles in the continuum

1996 ◽  
Vol 54 (4) ◽  
pp. 3078-3085 ◽  
Author(s):  
A. M. Mukhamedzhanov ◽  
M. Lieber
Keyword(s):  
Wave Function ◽  
Charged Particles ◽  
The Continuum

scholarly journals ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS

2008 ◽  
Vol 23 (09) ◽  
pp. 1405-1415 ◽  
Author(s):  
BRODIE CHAMPION ◽  
RICHARD L. HALL ◽  
NASSER SAAD
Keyword(s):  
Wave Function ◽  
Efficient Method ◽  
Iteration Method ◽  
Singular Potential ◽  
Asymptotic Form ◽  
Iteration Process ◽  
Asymptotic Iteration Method ◽  
Singular Potentials ◽  
Radial Schrödinger Equation ◽  
Arbitrary Dimensions

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials, such as V(r), valid for all ranges of coupling λ.

Complex eigenvalues in scattering theory

1959 ◽  
Vol 253 (1272) ◽  
pp. 16-36 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Excited States ◽  
Scattering Theory ◽  
Asymptotic Form ◽  
Outgoing Wave ◽  
Complex Energy ◽  
Channel One ◽  
Complex Eigenvalues ◽  
Relativistic Problem

The non-relativistic problem of scattering of a particle by a target possessing discrete excited states can be expressed in terms of ‘physical’ resonance states, i.e. solutions of the wave equation for complex energy in which in the asymptotic form of the wave function in each channel one of the two possible exponential terms (which for real energy represent the incoming and outgoing wave) vanishes. This representation is possible provided the interaction between the particles and the target vanishes exactly beyond a certain distance. If the interaction decreases exponentially a similar representation may in some cases still be obtained by analytic continuation; it contains also ‘redundant’ eigenstates in which the coefficient of one of the asymptotic waves tends to infinity. Possible generalizations of the method are discussed.

Asymptotic Form of the Wave Function for Three-Particle Scattering

1969 ◽  
Vol 178 (5) ◽  
pp. 2226-2228 ◽  
Author(s):  
J. NUTTALL ◽  
J. G. WEBB
Keyword(s):  
Wave Function ◽  
Asymptotic Form ◽  
Particle Scattering
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