Summary
In the present note we study in detail the case of the harmonic oscillator according to the « leapfrog » method of Moncrief and determine the coherent states of the corresponding annihilation operator in discrete time. The corresponding propagators in the Schrödinger and Heisenberg pictures are different.
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Jannussis, A. Quantum equations of motion in the finite-difference approach. Lett. Nuovo Cimento 40, 250–256 (1984). https://doi.org/10.1007/BF02751779
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DOI: https://doi.org/10.1007/BF02751779