What is meant by the periodicity of properties? What property of fluorescence indicates that it is a spin-allowed process? Does this property also explain why phosphorescence is not spin-allowed? What are shims in an NMR spectrometer and what is their purpose? Explain ...
where in the second equality, we exploited the fact that \(\chi _j(\textbf{r}; \textbf{R})\) is an eigenfunction of \(\mathcal {H}_e(\textbf{r}; \textbf{R})\). Neglecting the last two terms of the r.h.s., i.e., those related to the derivative of \(\chi _j(\textbf...
If one has an eigenfunction of the Laplacian, then we have the explicit solutions of the wave equation, which formally can be used to construct all other solutions via the principle of superposition. When one has vanishing initial velocity , the solution is given via functional calculus by ...
If one has an eigenfunction of the Laplacian, then we have the explicit solutions of the wave equation, which formally can be used to construct all other solutions via the principle of superposition. When one has vanishing initial velocity , the solution is given via functional calculus by ...
Given the parent function of g(x) = x^3, what change will occur when the function is changed to g(x) + 3? For the following, what is the result of acting the given operator on the given function? Is the function an eigenfunction or the operator? Operate \hat B = y + \frac{d...
Ψ x is local, but it has robust long-range phase ( )coherence unlike the fragile micro-quantum phases. Ψ x has phase rigidity and, therefore, does not ( )collapse like ψ x does into some eigenfunction ϕ j with real number eigenvalue j of a measurement observable corresponding to ...
Since the source function in this example, f=sin(πx), is an eigenfunction of the spectral Laplacian, the spectral solution is analytic in Ω and no boundary layer forms. For the Riesz solution, however, the boundary regularity decreases with α, resulting in the boundary singularities ...
EIGENFUNCTION EXPANSION METHOD FOR MULTIPLE SOLUTIONS OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH CUBIC POLYNOMIAL NONLINEARITY and differentiating twice, we obtain an equivalent second-order two-point boundary value problem (BVP) for the equilibrium solution [p.sup.*] = [p.sup.*](x) Linear...
Eigen-; designating a function or value which is an eigenfunction or eigenvalue. Good Reliable; sure A good investment. Proper Accurate, strictly applied. Good Valid or true A good reason. Proper Excellent, of high quality; such as the specific person or thing should ideally be. (Now often...
A state of a system that is represented by an eigenfunction of that system. Mode (computing) One of various related sets of rules for processing data; more generally, any state of the system associated with certain behaviours. In insert mode, characters typed are directly inserted into the buf...