Abstract
The unitary operations which can be generated on many particle states in non-relativistic quantum mechanics are discussed. These operations depend on an arbitrary external field which is in the experimenter's control, whereas the pairwise potential of interaction between the particles is fixed. The various kinds of systems ofN identical particles interacting via the potentials\(V_I = \sum\limits_{k,j} {r_{kj}^p w(r_{kj} )} \) are studied. For every system in question, the semigroup spanned by evolution transformations is proved to contain all the unitary operators in the Hilbert space of states. In particular, it is shown that the natural evolution operation can be reversed by a certain prescribed sequence of maneouvres involving only external fields.
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Waniewski, J. “Time inversion” and mobility of many particle systems. Commun.Math. Phys. 76, 27–37 (1980). https://doi.org/10.1007/BF01197108
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DOI: https://doi.org/10.1007/BF01197108