In 1929, J. von Neumann and E. P. Wigner showed that states with point eigenvalues $E\geq0$ could, nevertheless, be square integrable, i.e., would not resemble systems like an electron moving away from a center to infinity. In contrast, the authors provide an intuitive, classical interpretation of states which belong to non-normalizable states which are not elements of the continuous spectrum but obtain discrete eigenvalues when they reach infinity in finite time. For the complete localization, they conjecture about an intriguing interference effect, and it is the aim of this project to assist those to giants with the proof of their hypothesis.
Outline:
Resources:
- Über merkwürdige diskrete Eigenwerte, J. von Neumann and E. P. Wigner, Physikalische Zeitschrift 30, 465-467(1929)