Project Overview:

This is a report of our group’s study of Darboux Transformations and its role in the spectral analysis of one-dimensional Schrödinger operators.

• Developed the Hilbert space formalism for spectral analysis.
• Applied the method to three Schrödinger operator eigenvalue problems:
  • The simple harmonic oscillator.
  • The reflectionless potential.
  • The Coulomb potential.
• Explored broad implications in quantum mechanics and mathematical physics.

Click here to view the full project report (PDF).