Explicit Quantum Green Function for Scattering Problems in 2-D Potential
- URL: http://arxiv.org/abs/2112.01622v1
- Date: Wed, 1 Dec 2021 16:30:47 GMT
- Title: Explicit Quantum Green Function for Scattering Problems in 2-D Potential
- Authors: Brahim Ben Ali, Mohammed Tayeb Meftah
- Abstract summary: We present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space.
The system considered in this work is a quantum particle that have an energy E and moves in an axi-symmetrical potential.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we present a new result which concerns the derivation of the
Green function relative to the time-independent Schrodinger equation in two
dimensional space. The system considered in this work is a quantum particle
that have an energy E and moves in an axi-symmetrical potential. Precisely, we
have assumed that the potential V(r), in which the quantum particle moves, to
be equal to zero inside a disk (radius b) and to be equal a positive constant
V0 in a crown of internal radius b and external radius a (b < a) and equal zero
outside the crown (r > a). We have explored the diffusion states regime for
which E > V0. We have used, to obtain the Green function, the continuity of the
solution and of its first derivative at r = b and r = a. We have obtained the
associate Green function showing the resonance energies (absence of the
reflected waves) for the case E > V0.
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