Model Problems in Quantum Mechanics

Jiří Souček

From the dichotomy nonlocality vs which is the consequence of Bell Inequalities (BI) we shall choose the non-realism. We shall present here the modified Quantum Mechanics (modQM) in the axiomatic form. ModQM was introduced in [5] and we shall show its non-realism in the description of an internal measurement process. ModQM allows the restoration of locality, since BI cannot be derived in it. In modQM it is possible to solve: the measurement problem, the collapse problem, the problem of a local model for EPR correlations (see[5]). ModQM is a unique explicit realization of non-realism in QM. ModQM should be preferred as an alternative to the standard QM mainly since it restores the locality.

Emilio d’Emilio, Luigi E. Picasso

Emilio d’Emilio, Luigi E. Picasso

Jürg Fröhlich, Alessandro Pizzo

This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical isolated systems consisting of matter interacting with the radiation field is discussed and shown to correspond to a stochastic time-evolution of states of individual systems. The importance of dissipation for the successful completion of measurements is highlighted. To conclude, a solution of the ``Measurement Problem'' is sketched in an idealized model of a double-slit experiment.

Alexander P. Yefremov

Virtual Ring Theory implies replacement of a particle with a ghost ring endowed with certain standards that are used to measure distances and mechanical characteristics in integer numbers. This model is applied to three “classical” quantum-mechanical (QM) problems, 1D-box system, H-atom, and linear oscillator. It is shown that the relevant virtual geometric models entail the same energy levels as follow from the respective exact solutions of the Schrödinger equation.