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Applications of the Formalism-II
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
In classical mechanics, angular momentum of a system or body is related to its rotation in space. The angular momentum is a constant of motion when the net external torque acting on the system is zero. Thus, for a closed system, the angular momentum of a body is a conserved quantity due to isotropy of space. This isotropy means that the angular momentum of a body in a closed system does not vary when it is rotated as a whole in any manner in space. Generally, energy, momentum and angular momentum of a closed system are conserved quantities. Classically, the angular momentum of a particle of mass “m” is defined as: L→=r→×p→
Guiding neutral polar molecules by electromagnetic vortex field
Published in Journal of Modern Optics, 2020
Manipulating the equations of motion, one can derive a couple of formulas for the constants of motion. The first two are rather obvious. They are the velocity of the motion along the z-axis and the absolute value of the electric dipole moment: It should be noted that might not be a constant if relativistic effects were taken into account. This phenomenon was observed and derived in [16] for charged particles moving in an electromagnetic vortex field and later in combination with a constant magnetic field [30]. However, the model considered in the present paper is non-relativistic by definition since the electric dipole moment is not a relativistic concept.
Rigorous vibrational Fermi resonance criterion revealed: two different approaches yield the same result
Published in Molecular Physics, 2020
S. V. Krasnoshchekov, E. O. Dobrolyubov, M. A. Syzgantseva, R. V. Palvelev
The quantitative theory of vibrational resonance states should be connected to other physical phenomena affected by resonances. In particular, the concept of vibrational polyads is also very closely related to vibrational resonances because a manifold of coupled states has the common attribute – the identical polyad quantum number [45,56–60]. The conservation of the polyad quantum number for a manifold of close lying resonance states should have some physical significance, but so far such theory is not well developed because of its complexity from the quantum mechanical point of view. It should be noted that in classical mechanics the constants of motion include in addition to the energy, linear and angular momenta the less well-known Laplace-Runge-Lenz vector [61].