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
- URL: http://arxiv.org/abs/2304.03865v2
- Date: Tue, 11 Apr 2023 19:48:59 GMT
- Title: 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
- Authors: Li Hua Yu
- Abstract summary: We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process.
Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin frac12, with its magnetic moment in interaction with a magnetic field.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present a set of exact system solutions to a model we developed to study
wave function collapse in the quantum spin measurement process. Specifically,
we calculated the wave function evolution for a simple harmonic oscillator of
spin \frac{1}{2}, with its magnetic moment in interaction with a magnetic
field, coupled to an environment that is a bath of harmonic oscillators. The
system's time evolution is described by the direct product of two independent
Hilbert spaces: one that is defined by an effective Hamiltonian, which
represents a damped simple harmonic oscillator with its potential well divided
into two, based on the spin and the other that represents the effect of the
bath, i.e., the Brownian motion. The initial states of this set of wave
functions form an orthonormal basis, defined as the eigenstates of the system.
If the system is initially in one of these states, the final result is
predetermined, i.e., the measurement is deterministic. If the bath is initially
in the ground state,and the wave function is initially a wave packet at the
origin, it collapses into one of the two potential wells depending on the
initial spin. If the initial spin is a vector in the Bloch sphere not parallel
to the magnetic field, the final distribution among the two potential wells is
given by the Born rule applied to the initial spin state with the well-known
ground state width. Hence, the result is also predetermined. We discuss its
implications to the Bell theorem[1]. We end with a summary of the implications
for the understanding of the statistical interpretation of quantum mechanics.
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