Weak measurement of the kinetic and potential energies of the quantum harmonic oscillator subject to a ground state pre-selection

Abstract

We present the weak measurement of the kinetic and potential energies of the quantum harmonic oscillator that are pre-selected in its ground state and post-selected in a Gaussian wave packet with its peak at x = x₀ that is very far from the origin. It is found that the weak measurement may yield a negative weak value of kinetic energy for sufficient values of meter uncertainty and x₀. Such negative weak value does not arise from poles. On the other hand, the weak measurement of potential energy yields strictly positive weak value. We also present the consistency and interpretation of the measurement outcomes.