A dynamical model for wavefunction collapse via non-Hermitian Hamiltonian

Abstract

Ever since the formulation of quantum mechanics, there is very little understanding of the process of the collapse of a wavefunction. We have proposed a dynamical model to emulate the measurement postulates of quantum mechanics. We postulate that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse". We demonstrate this using a 2-level system and then extend it to an N-level system. For a 2-level system, we also demonstrate that the dynamics generated by the Lindblad master equation can be replicated as an incoherent sum of the evolution by two separate non-Hermitian Hamiltonians. I. INTRODUCTIONAny standard quantum mechanics course or textbook [1]-[2] begins with a set of postulates. Three of them are termed the "measurement postulates", which we are currently interested in. These are: P1. A wavefunction, upon measurement of an observable, will always "collapse" to one of the eigenstates of the operator corresponding to that observable.P2. The probability of collapse to a particular eigenstate depends on the probability amplitudes associated with each eigenstate in the linear decomposition of the wavefunction.P3. Any repeated measurement immediately after a collapse gives the same eigenstate.