Comments on the Classical Limit of Quantum Mechanics

Jorge Bernal, A. Martín-Ruiz, J. C. García-Melgarejo

Namit Anand

This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct for the limitation on the superposition of state vectors corresponding to different sectors of the Hilbert space, partitioned by a superoperator has a flaw as outlined below.

Ilki Kim, GERALD J. IAFRATE

A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why the square of the angular momentum in quantum mechanics is given by j(j+1) instead of just j^2, where j is the angular momentum quantum number.

Valia Allori, Nino Zanghı̀

Dipankar Home, S. Sengupta

Tomio Yamakoshi Petrosky, William C. Schieve

The nonlocal effect of quantum mechanics upon the classical chaos around the separatrix in a Hamiltonian system is investigated by extending the definition of the Melnikov function in the semiclassical approximation. It is shown that the quantum correction of the Melnikov function is related to the quantum fluctuation of the energy on the stable and unstable manifolds. This correction is a constant shift of the center of oscillation of the classical Melnikov function from zero. Because of this shift, the effect of quantum mechanics suppresses the classical chaos around the separatrix. Physical estimates are made of the magnitude of the quantum effect for a double-well oscillator system. As examples, we treat the case of the electron for the molecular scale and the proton for the nuclear scale, and also comment on the ammonia molecules ${\mathrm{NH}}_{3}$, ${\mathrm{ND}}_{3}$, and ${\mathrm{NT}}_{3}$.