Search

Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schrödinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem. It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction of the wave function. La meccanica quantistica con localizzazione spontanea (QMSL) è una modificazione stocastica recentemente proposta dell'equazione di Schrödinger aNcorpi in accordo sia con la microfisica che con la macrofisica. In questo lavoro la QMSL è applicata al problema della misurazione. Si mostra che la sostituzione della meccanica quantistica usuale con la QMSL ha il solo effetto di dar luogo a un'effettiva riduzione della funzione d'onda. Квантовая механика со спонтанной локализацией представляет недавно предложенную стохастическую модификациюN-частичного уравнения Шредингера, согласуюшуюся и с микрофизикой и с макрофизикой. В зтой равоте квантовая механика со спонтанной локализацией применяется к проблеме измерения. Показывается, что замена стандартной квантовой механики на квантовую механику со спонтанной локализацией приводит единственно к реальному упрощению волновой функции.

The continuity equation is formulated and studied in the framework of quantum mechanics with spontaneous localization. In the microscopic case the results of quantum mechanics are recovered.

The dynamical equation for the harmonic oscillator in Quantum Mechanics with Spontaneous Localization is solved. The evolution of the harmonic oscillator in such a theory is studied. In the case of atomic or nuclear dimensions the results of ordinary quantum mechanics are recovered.

Non-Hamiltonian evolution equations have been recently considered for the description of various physical processes. Among these types of equations the class which has been more extensively studied is the one usually referred to as quantum-dynamical semi-group equations (QDS). In particular an equation of the QDS type has been considered as the basis for a model, called quantum mechanics with spontaneous localization (QMSL), which has been shown to exhibit some very interesting features allowing us to overcome most of the conceptual difficulties of standard quantum theory. QMSL assumes a modification of the pure Schrödinger evolution by assuming the occurrence, at random times, of stochastic processes for the wave function corresponding formally to approximate position measurements. In this paper we investigate the consequences of modifying and/or enlarging the class of the considered stochastic processes, by considering the spontaneous occurrence of approximate momentum and of simultaneous position and momentum measurements. It is shown that the considered changes in the elementary processes have unacceptable consequences. In particular they either lead to drastic modifications in the dynamics of microsystems or are completely useless from the point of view of the conceptual advantages that one was trying to get from QMSL. The present work supports therefore the idea that QMSL, as originally formulated, can be taken as the basic scheme for the generalizations which are still necessary in order to make it appropriate for the description of systems of identical particles and to meet relativistic requirements.