Imperial College Second Year Project (2022)
This is a report of our group’s study of Darboux Transformations and its role in the spectral analysis of one-dimensional Schrödinger operators. We developed the Hilbert space formalism and applied the method to three Schrödinger operator eigenvalue problems: the simple harmonic oscillator, the reflectionless potential, and the Coulomb potential. This work has broad implications in quantum mechanics and mathematical physics.