Original research articleAdiabatic invariant of electron motion in slowly varying magnetic field studied with the squeezing mechanism in entangled state representation

Because the two coordinates of particle's guiding center of motion in uniform magnetic field do not commute, we think it is of necessity to study adiabatic invariant of electron motion in slowly varying magnetic field in the context of quantum mechanics. By constructing the entangled state representation which is the eigenvector of electron's coordinates and the squeezing mechanism of gyration radius, we directly reach the conclusion that the magnetic flux is adiabatic invariant in slowly varying magnetic field. We also compare this case with the adiabatic invariant of a pendulum whose string length is shortened very slowly.