Manuel Gadella
Some applications of the Birman-Schwinger operator in quantum mechanics
The energy-dependent Birman-Schwinger operator helps to solve, at least approximately, the eigenvalue problem associated with the Schrödinger equation, under the condition of having a negative definite potential (as for instance the Coulomb potential). Then, the eigenvalues of the Schrödinger equation are those values of the energy for which the Birman-Schwinger operator has an eigenvalue equal to one. For those cases in which the Birman-Schwinger operator is trace class, these solutions coincide with the zeroes of the Fredholm generalized determinant.
In the present talk, we shall discuss two examples of application of the method.
