Green Function on a Quantum Disk for the Helmholtz Problem

In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrödinger equation in two-dimensional space.The system considered in this work is a quantal particle that moves in an axi-symmetric potential.At rst, we have assumed that the potential V (r) to be equal to a constant V0 inside a disk (radius a) and to be equal to zero outside the disk.We have used, to derive the Green function, the continuity of the solution and of its rst derivative, at r = a (at the edge).Secondly, we have assumed that the potential V (r) is equal to zero inside the disk and is equal to V0 outside the disk (the inverted potential).Here, also we have used the continuity of the solution and its derivative to obtain the associate Green function showing the discrete spectra of the Hamiltonian.

• Green's function
• quantum disks
• Helmholtz equation
• time-independent Schrödinger equation
• axially symmetric potentials
• boundary conditions
• discrete spectrum
• two-dimensional quantum systems

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