In no-roll quantum cosmology, fixing the integration constant for potential energy yields a one-dimensional Hilbert space selecting Vilenkin's tunnelling wavefunction, while arbitrary values permit an infinite-dimensional space with a one-parameter family of boundary conditions at the singularity th
Self-adjoint extensions of operators and the teaching of quantum mechanics
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
For the example of the infinitely deep 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 physical situations. Some consequences are worked out, which could lead to experimental checks.
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Polymer quantization on compact spaces yields finite graph Hilbert spaces whose exact ring and box spectra recover Schrödinger QM as lattice spacing vanishes.
All separable Hilbert spaces of given dimension being isomorphic implies exactly six basic generalized coordinate operators and seven coordinate-momentum pairs via self-adjoint or Neumark extensions.
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All Hilbert spaces are the same: consequences for generalized coordinates and momenta
All separable Hilbert spaces of given dimension being isomorphic implies exactly six basic generalized coordinate operators and seven coordinate-momentum pairs via self-adjoint or Neumark extensions.