Self-adjoint extension in quantum mechanics and non-Rydberg spectra of one-dimensional hydrogen atom

We offer a beginner’s guide to the functional-analytical techniques in quantum mechanics, and cover its application to the 1D Coulomb problem. It is shown that the wave function at the diverging point of the Coulomb potential is mathematically described by three-parameter family of generalized connection conditions. A scheme is devised to physically implement the generalized conditions, which provides the way to experimentally realize non-Rydberg spectra in 1D Hydrogen atom.

Schedule:
Part 1, Self-adjoint extension of Hilbert space operator
Part 2, 1D Coulomb problem