Theoretical analysis reveals how self-adjoint extensions resolve operator paradoxes in the infinite well potential, highlighting symmetry constraints for physical Hamiltonians.
For the example of the infinite well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the momentum and the Hamiltonian operators in different settings. Additional physical requirements such as parity, time reversal, and positivity are used to restrict the large class of self-adjoint extensions of the Hamiltonian.
No takes yet. Share an insight, caveat, or question.
Bonneau et al. (2001) studied this question.