Schrodinger equation energy spectrum

The one-electron Hamiltonian operator h = h +v, with kinetic energy operator, generates a complete spectrum of orbitals according to the Schrodinger equation... 

The typical way to open a billiard is to attach some reservoirs with continuous energy spectrum, for example, the leads or microwave waveguides, as shown in fig. 3 below. Full information about the scattering properties of the billiard is given by the scattering wave function which is a solution of the Schrodinger equation Hip = Exp with the total Hamiltonian... 

Then, the energy spectrum of the system is described by the stationary Schrodinger equation... 

In order to calculate the absorption spectrum in the time-independent approach one solves the time-independent Schrodinger equation for a series of total energies and evaluates the overlap of the total continuum wavefunction, defined in (2.70), with the bound wavefunction of the parent molecule, ( tot(E) Pio I o(Ei)). Any structures in the spectrum are thus related to the energy dependence of the stationary wavefunction "Jftot(E). As illustrated schematically in Figure 7.4 for the one-... 

L. Gr. Ixaru and M. Rizea, A Numerov-like scheme for the numerical solution of the Schrodinger equation in the deep continuum spectrum of energies, Comput. Phys. Commun., 1980, 19, 23-27. 

Another indirect technique, which enables one to calculate the resonance spectrum for many energies simultaneously, is the wave packet method [163-168], used, for example, in studies of non-rotating [47,169] and rotating [52] HCO, HO2 [170] and H2O [71]. One iteratively solves the time-dependent Schrodinger equation, Eq. (10),... 

For the parameters 8 = 2Qq and <2max = O0, corresponding to the path (a) on the surfaces in Fig. 19, we show in Fig. 20 the solution of the semiclassical Schrodinger equation (321). It features a STIRAP-like process inducing a complete population transfer for this choice of the delays. Two zones of the quasi-energy spectrum associated with the surfaces of Fig. 19 are pictured as a function of time in Fig. 21b. We notice that the state 11 0,0) is... 

As a result of solving the Schrodinger equation for the model Hamiltonian (9.3) one gets anharmonic frequencies and relative IR intensities (if the dipole moment function is available) in the particular region of the IR spectrum [23-25]. It should be noted, however, that in many theoretical studies only the energy spectrum of the model 2D Hamiltonian was considered [26, 27]. 

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