On Wave Function Collapse in Quantum Mechanics in the case of a Spin system having three anticommuting operators
We use a two states quantum spin system S, and thus considering the particular case of three anticommuting elements and the measurement of 푒3. We evidence that, during the wave collapse, we have a transition of standard commutation relation of the spin to new commutation relations and this occurs during the interaction of the S system with the macroscopic measurement system M. The reason to accept such viewpoint is that it causes the destruction of the interferential factors and of the fermion creation and annihilation operators of the S system without recourse to further elaborations based on the use of Hamiltonians or other methods. By this the formulation we propose a new method in attempting to solve the problem of wave function collapse. The concept of Observable, in use in standard quantum mechanics, is resolved in an abstract entity to which is connected a linear hermitian operator that signs mathematically the operation that we must perform on the wave function in order to obtain the potential and possible values of the observable. It does not commute with a number of other operators characterizing the system and the non-commuting rules have a fundamental role in quantum mechanics. They have a logic that must be analyzed in each phase of the non-measuring and the measuring processes. When we consider the dynamics of wave function collapse we must an account that the observed Observable becomes a number, with proper unity of measurements, during the measurement, thus the linear hermitian operator to which is connected before the measurement, disappears and in its place, it appears a new operator that maintains the non-commutativity with the other operators to which the old and disappeared operator was connected.