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We present a set of exact system solutions to a model we developed to studywave function collapse in the quantum spin measurement process. Specifically,we calculated the wave function evolution for a simple harmonic oscillator ofspin \frac{1}{2}, with its magnetic moment in interaction with a magneticfield, coupled to an environment that is a bath of harmonic oscillators. Thesystem's time evolution is described by the direct product of two independentHilbert spaces: one that is defined by an effective Hamiltonian, whichrepresents a damped simple harmonic oscillator with its potential well dividedinto two, based on the spin and the other that represents the effect of thebath, i.e., the Brownian motion. The initial states of this set of wavefunctions form an orthonormal basis, defined as the eigenstates of the system.If the system is initially in one of these states, the final result ispredetermined, i.e., the measurement is deterministic. If the bath is initiallyin the ground state,and the wave function is initially a wave packet at theorigin, it collapses into one of the two potential wells depending on theinitial spin. If the initial spin is a vector in the Bloch sphere not parallelto the magnetic field, the final distribution among the two potential wells isgiven by the Born rule applied to the initial spin state with the well-knownground state width. Hence, the result is also predetermined. We discuss itsimplications to the Bell theorem[1]. We end with a summary of the implicationsfor the understanding of the statistical interpretation of quantum mechanics.

A model of wave function collapse in a quantum measurement of spin as  the Schroedinger equation solution of a system with a simple harmonic  oscillator in a bath