Symbolizing states and events in quantum mechanics

Carsten Held

pp. 193-209

in: Massimo Ferrari, Ion-Olimpiu Stamatescu (eds), Symbol and physical knowledge, Berlin, Springer, 2002

Abstract

Modern textbooks in statistical mechanics sometimes present classical and quantum-mechanical formalisms in an exactly parallel fashion. At the outset, pure states are symbolized by either phase space points or Hilbert space vectors (or, more generally, rays); observables by either real-valued functions or self-adjoint operators; and their values by either values of the functions or expectation values of the operators. Consequently, also time expansions of states and the values of observables have comparable expressions (see, e.g., Römer and Filk, 1994, p. 47–48). This way of parallelizing the formalisms expresses the general view that they are parallel in the sense that there is one set of symbols functioning in the same fashion in both classical and quantum physics, i.e., symbols describing a system's physical state, as well as symbols designating observables and their values.