The Hagedorn–Hermite Correspondence

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dc.contributor.authorOhsawa, Tomoki
dc.contributor.utdAuthorOhsawa, Tomoki
dc.date.accessioned2019-09-27T16:13:42Z
dc.date.available2019-09-27T16:13:42Z
dc.date.created2018-07-17
dc.descriptionFull text access from Treasures at UT Dallas is restricted to current UTD affiliates (use the provided Link to Article).
dc.description.abstractWe investigate the relationship between the semiclassical wave packets of Hagedorn and the Hermite functions by establishing a relationship between their ladder operators. This Hagedorn–Hermite correspondence provides a unified view as well as simple proofs of some essential results on the Hagedorn wave packets. Particularly, we show that Hagedorn’s ladder operators are a natural set of ladder operators obtained from the position and momentum operators using the symplectic group. This construction reveals an algebraic structure of the Hagedorn wave packets, and explains the relative simplicity of Hagedorn’s parametrization compared to the rather intricate construction of the generalized squeezed states. We apply our formulation to show the existence of minimal uncertainty products for the Hagedorn wave packets, generalizing Hagedorn’s one-dimensional result to multi-dimensions. The Hagedorn–Hermite correspondence also leads to an alternative derivation of the generating function for the Hagedorn wave packets based on the generating function for the Hermite functions. This result, in turn, reveals the relationship between the Hagedorn polynomials and the Hermite polynomials. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
dc.description.departmentSchool of Natural Sciences and Mathematics
dc.identifier.bibliographicCitationOhsawa, T.. 2018. "The Hagedorn–Hermite Correspondence." Journal of Fourier Analysis and Applications 25(4): 1-40, doi: 10.1007/s00041-018-9633-3
dc.identifier.issn1069-5869
dc.identifier.issue4
dc.identifier.urihttps://hdl.handle.net/10735.1/6924
dc.identifier.volume25
dc.language.isoen
dc.publisherBirkhäuser Boston
dc.relation.urihttp://dx.doi.org/10.1007/s00041-018-9633-3
dc.rights©2018 Springer Science+Business Media, LLC, part of Springer Nature
dc.source.journalJournal of Fourier Analysis and Applications
dc.subjectWave pckets
dc.subjectSymplectic groups
dc.titleThe Hagedorn–Hermite Correspondence
dc.type.genrearticle

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