%0 Journal Article %1 delaMadrid2005Role %A de la Madrid, %D 2005 %K resonance %R 10.1088/0143-0807/26/2/008 %T The role of the rigged Hilbert space in Quantum Mechanics %U http://dx.doi.org/10.1088/0143-0807/26/2/008 %X There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.

@article{delaMadrid2005Role, abstract = {{There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.}}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {de la Madrid}, biburl = {https://www.bibsonomy.org/bibtex/2bab5e90228b3d95b5100f06fbcb51acf/cmcneile}, citeulike-article-id = {5159616}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0502053}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0502053}, citeulike-linkout-2 = {http://dx.doi.org/10.1088/0143-0807/26/2/008}, comment = {This was discussed in a nuclear structure seminar. It is perhaps a way to deal with resonances. I am not sure that this is mentioned in this paper though. See alsp http://en.wikipedia.org/wiki/Rigged\_Hilbert\_space}, day = 9, doi = {10.1088/0143-0807/26/2/008}, eprint = {quant-ph/0502053}, interhash = {e3baf885502ee80ed35df45da01eaf3c}, intrahash = {bab5e90228b3d95b5100f06fbcb51acf}, keywords = {resonance}, month = feb, posted-at = {2009-07-15 16:01:38}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{The role of the rigged Hilbert space in Quantum Mechanics}}, url = {http://dx.doi.org/10.1088/0143-0807/26/2/008}, year = 2005 }