Tomasz Stachowiak 氏
The usual approaches to finding energy eigenvalues in quantum systems involve direct diagonalization or solving constraints given by boundary conditions, possibly at infinity. However, instead of working directly with functional equations, in many systems of quantum optics it is possible to translate those requirements into relations between elements of the monodromy group of certain associated differential equations. This follows from the simple formal assumption that the wavefunctions belong to the Bargmann Hilbert space. As the procedure relies on definite contour integrals and matrix algebra, it can also easily be implemented numerically.