Функция Грина квантовой частицы, движущейся в двумерном кольцевом потенциале

In this work, we present a new result which concerns the obtainment of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a 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 particle moves, to be equal to zero inside an annular region (radius b) and to be equal a positive constant (V0) in a crown of internal radius b and external radius a (b a). We have explored the bounded states regime for which (E < V0). We have used, to obtain the Green function, the continuity of the solution and of its derivative at (r = b) and (r = a): We have obtained the associate Green function and the discrete spectra of the Hamiltonian in the region (r < b)

• Green's function
• time-independent Schrödinger equation
• axially symmetric potentials
• discrete spectrum
• Hamiltonian spectrum

• Spectral Theory in Mathematical Physics
• Quantum Mechanics and Non-Hermitian Physics
• Differential Equations and Boundary Problems
• Green's function
• time-independent Schrödinger equation
• axially symmetric potentials
• discrete spectrum
• Hamiltonian spectrum
• Mathematical Physics
• Atomic and Molecular Physics, and Optics
• Applied Mathematics
• Mathematics
• Physics and Astronomy