vanhees71 said:A very good book on more formal mathematical scattering theory is.
R. Newton, Scattering Theory of Waves and Particles
A Jost matrix is a mathematical tool used in quantum mechanics to describe the behavior of a quantum system. It is a matrix representation of the Hamiltonian operator, which represents the total energy of the system.
The Jost matrix is used to find the eigenvalues and eigenvectors of the Hamiltonian operator, which can provide information about the energy levels and states of the quantum system. It is also used to calculate scattering amplitudes and study the dynamics of the system.
The Jost matrix has many applications in physics, particularly in the fields of quantum mechanics, nuclear physics, and condensed matter physics. It is used to study the behavior of atoms, molecules, and particles, as well as the interactions between them.
There are many books available on the Jost matrix, but some popular choices include "The Jost Function and Its Applications" by F. Gesztesy and H. Holden, "Scattering Theory: The Quantum Theory of Nonrelativistic Collisions" by John R. Taylor, and "Introduction to Quantum Mechanics" by David J. Griffiths.
Yes, a strong understanding of linear algebra, complex analysis, and differential equations is necessary to fully understand the Jost matrix. It is recommended to have a solid foundation in mathematics before delving into the study of the Jost matrix.