We study wave equations with energy-dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations can be handled as evolution equation of quantum ...
IN Dirac's "Quantum Mechanics" the "equation of motion" satisfied by any observable , ξ not involving the time explicitly is whereis the Hamiltonian. The conservation of energy, whendoes not involve the time explicitly, is deduced from this by putting ξ =, giving= 0.A. LEES...
We provide a mild solution for the wave equation in terms its Fourier expansion. We calculate the expected energy and give asymptotic results for the expected energy for large and small times and as the Hurst parameter, H, approaches 1/2. These results are phrased in terms of the norms of...
In this paper we study the behavior of the energy of solutions of the wave equation with localized damping and an external force on compact Riemannian manifold with boundary. Under the Geometric Control Condition of Bardos et al. (1992) [4] and certain condition on the force, we prove that...
interaction of particlesnonlinear parabolic-elliptic systemsThe Schrdinger equation with the two-Coulomb-center potential plus the harmonic-oscillator one is solved by the comparison-equation method for large intercenter distances. Asymptotic expansions for energy levels and wave functions are obtained....
摘要: Applying a class of quadratic forms introduced by Manfrin (Port. Math. 65(4):447–484, 2008), we study the asymptotic behavior, as t → +∞, of the energy of the solutions to the Cauchy problem for wave equations with time dependent propagation speed.关键词:...
The energy of a photo is related to its frequency and its wavelength. It is directly proportional to frequency and inversely proportional to wavelength. To find energy from wavelength, use the wave equation to get the frequency and then plug it into Planck's equation to solve for energy. ...
The aim of this research is to develop an innovative approach for electric power conversion of the vast ocean wave energy. A floating-buoy wave energy converter (WEC) using hydrostatic transmission (HST), which is shortened as HSTWEC, has been proposed to enhance the wave energy generation from...
FINITE TIME BLOW-UP FOR THE NONLINEAR FOURTH-ORDER DISPERSIVE-DISSIPATIVE WAVE EQUATION AT HIGH ENERGY LEVEL. In this paper, we investigate the initial boundary value problem of the nonlinear fourth-order dispersive-dissipative wave equation. By using the concavity... RUNZHANG - 《International Journ...
To determine the energy of a wave from its wavelength, we need to combine Planck's equation with wavelength equation. The resulting expression E = hc/λ is used as a wavelength formula. Here, h is Planck's constant and c is the speed of light. So energy