The correspondence principle between classical and quantum quantities

Quanhui Liu, B Hu

The famous Gordon formula for matrix element ⟨ n ', l | r | n , l -1⟩ is transformed into a new form which can be easily treated when n ', n and l are all large. Then its asymptotic expression is derived which turns out to be that obtained from Heisenberg's correspondence principle. Finally, its classical limit form is used to construct classical quantities x , y and z representing a singe Keplerian orbit in terms of a Fourier series of time variable t .

A. O. Bolivar

Martin Jähnert

Wu Chuang

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.

Zhi Zhang

According to 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.Applying HCP to Dirac equations in relativistic realm,for the relativistic free particle or the charged particle moving in a constant magnetic field,it is shown that quantum operators in Dirac theory reduces to the classical quantities in the classical limit and the classical limit of quantum expectation value is the time average of the classical quantity.