Abstract
The propagator of an harmonic oscillator in a constant magnetic field is given in closed holomorphic form. The analytical expression of the unitary map is evaluated, which converts the holomorphic representation into the coordinate one. This is applied to obtain a closed form of the Feynman’s propagator in polar coordinates. The procedure is of general validity and can be extended to many non interacting oscillators.
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Ramaglia, V.M., Preziosi, B., Tagliacozzo, A., Ventriglia, F. (1989). Quantum Harmonic Oscillator in a Magnetic Field: An Example of Holomorphic Representation. In: Doni, E., Girlanda, R., Parravicini, G.P., Quattropani, A. (eds) Progress in Electron Properties of Solids. Physics and Chemistry of Materials with Low-Dimensional Structures, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2419-2_34
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DOI: https://doi.org/10.1007/978-94-009-2419-2_34
Publisher Name: Springer, Dordrecht
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