Dynamics of quantum transition of a particle in a potential well

Background and Objectives: Usually the quantum transition from the stationary state to another stationary state is considered instantaneous. The quantum transition consists of a perturbation of the initial state and a reduction to the final state. Therefore, an instantaneous change in the particle localization corresponding to the transition from one wave function to another at superluminal speed is unacceptable. Also, a wave train of radiation, if it occurs during the transition, cannot arise instantly. This article proposes a dynamical model of quantum transition in which the reduction to the final state occurs dynamically but not instantly. Methods: The probability amplitudes of the modes in the intermediate state arising from the initial stationary state were determined by solving a system of differential-algebraic equations. The reduction of the intermediate state to the final mode was simulated by piecewise continuous evolution with periodic zeroing of the imaginary part of the wave function. Conclusion: This model has been applied to a particle in a potential well with negative energy. The potential is chosen as the square of the hyperbolic cosecant. Such a three-level well contains two qubits. The time scale of reduction to stationary states of these qubits is hundreds of periods corresponding to the Bohr frequencies of transitions. So the quantum transition is a process with a dynamical perturbation of the initial state and a dynamical reduction to the final state. 

quantum transitions, dynamic reduction, dynamics of the quantum transition, projection postulate, qubits in the quantum well