Quantum States for Quantum Measurements

This work introduces a different way to understand the concept of quantum state (QS) with incidence on the concept of measurement. The mathematical architecture is unchanged; abstract QSs are elements of a linear vector space over the field of complex numbers. Inertial frames mediate introduction of configuration space (CS); the number of degrees of freedom defining the material system characterizes the CS dimension. A rigged Hilbert space permits projecting abstract quantum states leading to generalized wavefunctions. CS coordinates do not map out particle positions, but wavefunctions retain the character of abstract quantum states; operators act on QS can yield new quantum states. Given a basis, quantum states are defined by the set of nonzero amplitudes. QSs are submitted to quantum probing; amplitudes control response to external probes. QSs are sustained by the material system, yet they are not attributes (properties) of their elementary constituents; these latter must be present yet not necessarily localized. With respect to previous views on quantum measurement, the one presented here shows characteristic differences, some of which are discussed below.