momentumIn this paper, the energy and momentum operator substitution method derived from the Schrödinger equation is used to list all possible light and matter wave equations, among which the first light wave equation and relativistic approximation equation are proposed for the first time. We ...
, and k is the space part of the 4-vector k λ ≡ (k, k) , we look for the operator p 0 such that p 0 w k = k w k . (One can see by inspection of (10a) that w k is not an eigenfunction of the “radial momentum operator” p r ≡ −ir −1/2 ∂ r r 1/2...
Energy momentum tensor and operator product expansion in local causal perturbation theory - Prange - 2000 () Citation Context ...onological product) from the condition of gauge invariance. Gravitation can be also analysed in this framework [32], [38], [39], [58], etc. Finally, the ...
Energy and Momentum as Observables in Quantum Field Theory - Borchers - 1966 () Citation Context ...r H is an observable. For instance, if oe t represents the time evolution of the system, then `oe �� t is inner' means that the Hamiltonian exists as an observable in the (GNS)...
(2) for x(t) we can obtain the oscillator momentum operator p(t) from the standard relation p(t)=Mx˙(t). It allows to calculate the mean kinetic Ek(t) = 〈p2(t)〉/2M and potential Ep(t)=Mω02⟨x2(t)⟩/2 energy of the quantum oscillator. In the long time limit,...
low energies. While such term is marginal in the usual sense, it is irrelevant relative to the generalised conformal structure. Indeed, we will see that it induces a beta function for the quartic coupling and we will discuss its contribution to the 2-point function of the energy-momentum ...
This paper provides a mass, momentum, and energy flux conservation analysis between the linear and nonlinear steady-state wave groups. Convergent high-order solutions for nonlinear wave groups with multiple steady-state near resonances in deep water have been obtained by means of the homotopy analysis...
In our case, the energy (linked to the Hamiltonian operator 𝐻̂H^) and the momentum (linked to the momentum operator 𝑝̂p^) can be simultaneously defined when [𝐻̂,𝑝̂]=0[H^,p^]=0. In the position representation, knowing that the Hamiltonian operator is the sum of ...
aThe overall histogram of the 2050 shares of solar PV.bThe shares solar PV depending on who pays for storage costs (variable renewable energy (VRE) sources, or the grid operator). Box plot elements: Centre line: median, box limit: upper and lower quartiles, whiskers: 1.5x interquartile ra...
This paper develops and applies the energy-momentum method to the problem of nonlinear stability of relative equilibria. The method is applied in detail to the stability of uniformily rotating states of geometrically exact rod models, and a rigid body with an attached flexible appendage. Here, the...