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Inertial and gravitational mass in quantum mechanics

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Abstract

We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.

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Authors and Affiliations

  1. Institut für Quantenphysik, Universität Ulm, Albert-Einstein-Allee 11, 89081, Ulm, Germany

    E. Kajari, N. L. Harshman & W. P. Schleich

  2. Department of Physics, American University, 4400 Massachusetts Ave., Washington, NW, 20016-8058, USA

    N. L. Harshman

  3. Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    E. M. Rasel

  4. Physics Department, Royal Institute of Technology, KTH, Stockholm, Sweden

    S. Stenholm

  5. Laboratory of Computational Engineering, HUT, Espoo, Finland

    S. Stenholm

  6. Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799, München, Germany

    G. Süßmann

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  1. E. Kajari
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Correspondence to W. P. Schleich.

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Kajari, E., Harshman, N.L., Rasel, E.M. et al. Inertial and gravitational mass in quantum mechanics. Appl. Phys. B 100, 43–60 (2010). https://doi.org/10.1007/s00340-010-4085-8

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  • DOI: https://doi.org/10.1007/s00340-010-4085-8

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