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Supersymmetric Schrödinger operators: an alternative approach using pseudo-differential operators

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Abstract

An asymptotic method based on the calculus of pseudo-differential operators is used to derive the well-known relations between one-particle supersymmetric partner Hamiltonians. This alternative approach will be applied to one of the standard examples of supersymmetric quantum mechanics, where all the known analytical results will be reproduced. We also note a fundamental uncertainty relation between an operator and its formal left and right inverses.

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Acknowledgements

The author would like to thank the Mandelstam Institute for Theoretical Physics (MITP) and the DST-NRF Centre of Excellence in Strong Materials (CoE-SM) at the University of the Witwatersrand for support.

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  1. School of Physics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

    Alexander Quandt

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  1. Alexander Quandt
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Correspondence to Alexander Quandt.

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Quandt, A. Supersymmetric Schrödinger operators: an alternative approach using pseudo-differential operators. Quantum Stud.: Math. Found. 8, 205–215 (2021). https://doi.org/10.1007/s40509-020-00239-1

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