Search results for "Discrete spectrum"
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The closed form of the second-order energy shift for the discrete spectrum of atomic hydrogen
2004
The closed form of the second-order energy shift for the discrete spectrum of atomic hydrogen is obtained, which allows us to evaluate the level shift in both cases, when the intermediate states are in continuum and in the discrete spectrum, except the resonances. The values of the second-order shift of the energy of the ground state calculated by us are in good agreement with those obtained by us and other authors using the nonperturbative Floquet method in average up to a radiation intensity of 1015 W cm−2.
Weyl Asymptotics for the Damped Wave Equation
2019
The damped wave equation is closely related to non-self-adjoint perturbations of a self-adjoint operator P of the form $$\displaystyle P_\epsilon =P+i\epsilon Q. $$ Here, P is a semi-classical pseudodifferential operator of order 0 on L2(X), where we consider two cases: X = Rn and P has the symbol P ∼ p(x, ξ) + hp1(x, ξ) + ⋯ . in S(m), as in Sect. 6.1, where the description is valid also in the case n > 1. We assume for simplicity that the order function m(x, ξ) tends to + ∞, when (x, ξ) tends to ∞. We also assume that P is formally self-adjoint. Then by elliptic theory (and the ellipticity assumption on P) we know that P is essentially self-adjoint with purely discrete spectrum. X is a com…