Abstract
We investigate a possible form of Schrödinger’s equation as it appears to moving observers. It is shown that, in this framework, accelerated motion requires fictitious potentials to be added to the original equation. The gauge invariance of the formulation is established. The example of accelerated Euclidean transformations is treated explicitly, which contain Galilean transformations as special cases. The relationship between an acceleration and a gravitational field is found to be compatible with the picture of the ‘Einstein elevator’. The physical effects of an acceleration are illustrated by the problem of the uniformly-accelerated harmonic oscillator.
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Hurley, D.J., Vandyck, M.A. \(\mathfrak{D}\)-Differentiation in Hilbert Space and the Structure of Quantum Mechanics Part II: Accelerated Observers and Fictitious Forces. Found Phys 41, 667–685 (2011). https://doi.org/10.1007/s10701-010-9509-0
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DOI: https://doi.org/10.1007/s10701-010-9509-0