LippmannSchwinger
Lippmann-Schwinger equation is a fundamental equation in quantum mechanics, named after Hans Bethe, who derived it from the work of Hans Bethe and Julian Schwinger. It provides a way to express the wave function of a quantum system in terms of its interaction with a reference system. The equation is particularly useful in the study of scattering processes, where it allows for the calculation of the scattering amplitude without explicitly solving the full Schrödinger equation.
The Lippmann-Schwinger equation can be written as:
ψ = φ + G0Vψ
where ψ is the wave function of the interacting system, φ is the wave function of the reference
where E is the energy of the system, H0 is the Hamiltonian of the reference system, and
The Lippmann-Schwinger equation can be solved iteratively, leading to a series expansion known as the Born
In summary, the Lippmann-Schwinger equation is a powerful tool in quantum mechanics, providing a way to calculate