A special transform for curved magnetic fields. Joint work with W. Klink

Professor Emeritus Palle Jorgensen

Abstract: The principal result is an explicit diagonalization of the sub-Laplacian L of the Heisenberg group G (of the one-dimensional harmonic oscillator), and their generalizations. Previously obtained results by Jorgensen are used; - on spectral properties of Lie theory sub-Laplacians L. Finally, an adapted Lax pair is used to find operators unitarily equivalents to L. Context: the QM Hamiltonians for a constant magnetic field and a linearly varying magnetic fields, respectively. Citations. Jorgensen, Palle E. T.; Klink, William H. Spectral transform for the sub-Laplacian on the Heisenberg group. J. Analyse Math. 50 (1988), 101-121. Jorgensen, P. E. T.; Klink, W. H. Quantum mechanics and nilpotent groups. I. The curved magnetic field. Publ. Res. Inst. Math. Sci. 21 (1985), no. 5, 969-999.

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