Trace class operators and states in <i>p</i>-adic quantum mechanics

Within the framework of quantum mechanics over a quadratic extension non-Archimedean field p-adic numbers, we provide definition state relying on general algebraic approach and model probability theory. As in standard complex case, distinguished set physical states are related to notion trace for certain class bounded operators and, fact, show that one can define suitable space setting, as well. The analogies, but also several (highly non-trivial) differences, with respect case Hilbert analyzed.