Schrodinger uncertainty relation for a quantum oscillator in a thermostat

We introduce the Schrodinger correlator as the holistic characteristic of two types of fluctuation correlations in quantum dynamics and in statistical thermodynamics. We are the first to derive it using methods of thermolield dynamics for the coordinate-momentum variables of a quantum oscillator in a thermostat. We show that the obtained value ensures that the Schrodinger uncertainty relation becomes an equality at all temperatures. We End that the thermal equilibrium for the quantum oscillator has the sense of the thermal correlated coherent state and can be adequately described by a wave function with temperature-dependent amplitude and phase.