Quantum and Classical Correspondence for Klein-Gordon Equation in Magnetic Field

In the quantum field,due to Bohr correspondence principle,quantum mechanics go to classical mechanics in large quantum number.Based upon Heisenberg correspondence principle,quantum matrix element of a Hermitian operator reduces to the coefficient of Fourier expansion of the corresponding classical quantity in the classical limit.Using Heisenberg correspondence principle,quantum-classical correspondence of particles in magnetic is studied.Applying Heisenberg correspondence principle in relativistic realm,the exact wave functions of Klein-Gordon equation are obtained for particles in magnetic with quantum matrix element in a rectangular coordinate system of new representation.It turns out that in the classical limit matrix elements of quantum operators reduces to the classical solutions and with classical approach,the coordinate is cyclical variation with time,the orbit of particles is a circle,and the movement is uniform circular motion in uniform magnetic field.