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N = 2j+1 if there is no conserved k independent parity. Otherwise N is the dimension of an irreducible representation of U0 and V.
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enm,eik) = enk δmi + ein δmk + ekm δni + emi δnk
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Clearly, not all of these constants are independent; we do not know whether all constants of the motion can be written in this form.
In the case (2) Vnm(k = 0) is tridiagonal because there exists a conserved k independent parity.
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Haake, F., Kuś, M., Scharf, R. (1987). Quantum chaos for kicked spins. In: Ehlotzky, F. (eds) Fundamentals of Quantum Optics II. Lecture Notes in Physics, vol 282. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18035-4_56
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DOI: https://doi.org/10.1007/3-540-18035-4_56
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