quantum mechanicsrotationIt is the purpose of this paper to derive the general form of the Schrdinger equation when the configuration of a system is specified partly by generalized coordinates and partly by a continuous group of transformations. Unlike generalized coordinates, where a configuration is...
3. Some specifics of the implementation of permutational and rotational symmetry in quantum mechanics are discussed in section “The Symmetries of the Clamped Nuclei Electronic Hamiltonian.” 4. A similar requirement must be placed on the denominator in Eq. 12 of Kutzelnigg uc2007) for the equat...
In quantum mechanics, the position-momentum uncertainty principle Δx⋅Δp≥12 can be proven from the properties of the Fourier transform for conjugate variables1. In the early years of quantum mechanics, energy and time were believed to be related similarly, by a so-called time-energy uncerta...
This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and
” (ibid.) This is true even in quantum mechanics (Lombardi et. al.2010, 99). In classical mechanics, the Lagrangian is invariant under rotations and translations, but not under boosts (Finkelstein1973, 106–107). Be careful. Landau and Lifshitz’s famous text on mechanics says that “the...
A complete description of the dynamics of any molecular system is contained in the Hamiltonian H, which is the energy operator in quantum mechanics or the energy function in classical mechanics. In general, the Hamiltonian is a function of the electronic and nuclear degrees of freedom, as is th...
The main focus is on periodic orbits and their neighbourhood, as this approach is especially suitable as an introduction to the implications of the theory of chaos in quantum mechanics, which are discussed in the last three chapters.
Quantum Mechanics for Hamiltonians Defined as Quadratic Forms Quantum Mechanics for Hamiltonians Defined as Quadratic Forms by Barry Simon Princeton Series in Physics Princeton University Press Princeton, New Jersey *1971 Copyright © 1971, by Princeton University Press All rights reserved L.C. Card:...
Condensed Matter - Statistical MechanicsCondensed Matter - Mesoscale and Nanoscale PhysicsCondensed Matter - Soft Condensed MatterCondensed Matter - SuperconductivityThe quantum Josephson Hamiltonian of two weakly linked Bose-Einsteincondensates is written in an overcomplete phase representation, thus avoidingthe...
(quantum mechanics) A mode of description of a system in which the time dependence is carried partly by the operators and partly by the state vectors, the time dependence of the state vectors being due entirely to that part of the Hamiltonian arising from interactions between particles. Also ...