Bound-state energies calculation

Orthogonal Polynomial Expansion of the Spectral Density Operator and the Calculation of Bound State Energies and Eigenfunctions. 

Time-to-Energy Fourier Resolution Method for Calculating Bound State Energies and Wavefunctions. 

For our exploratory calculation we use Guaussian type wave functions to find optimal bound states in the three and four particle case. Then we are able to calculate the perturbative expression for the shift of the bound states energy... 

Model calculations (e.g. [4]) predict that TqD exhibits resonances at the bound state energies of the QD, while aQp exhibits an interesting variation... 

Variational calculation of bound-state energies and wavefunctions... 

In order to calculate bound-state energies and the corresponding eigenfunctions we expand I>(R,r) according to... 

The calculation of bound-state energies is part of molecular spectroscopy. Many efficient methods and computer codes have been developed... 

The theory outlined above can be used to calculate the exact bound-state energies and wavefunctions for any triatomic molecule and for any value J of the total angular momentum quantum number. We can solve the set of coupled equations (11.7) subject to the boundary conditions Xjfi (R Jp) —> 0 in the limits R —> 0 and R — oo (Shapiro and Balint-Kurti 1979). Alternatively we may expand the radial wavefunctions in a suitable set of one-dimensional oscillator wavefunctions ipm(R),... 

In order to calculate the bound-state energies one expands the two-dimensional wavefunction in terms of products of suitably chosen, onedimensional basis functions (fn(Ri), = 1,2, which describe the vibration of the two OH entities within H20(X). Because the Hamiltonian is symmetric with respect to the interchange of the two bond distances, the... 

In view of the fundamental nature of the system more extensive and more precise data would be highly desirable as a test for bound state QED calculations. With the exception of the 1S-2S energy difference measurement, which is limited in precision by the laser wavelength measurement, all present experiments suffer from low statistics due to the small number of Ps atoms. It seems therefore worthwile discussing recent advances of increased Ps production and in parti-cular methods to populate the metastable 2 Sj state, which could serve as a basis for excited state spectroscopy. While laser excitation of states above n=2 from the ground state requires wavelengths between 205 nm (Lg) and 182 nm (ionization limit), which are very difficult to obtain with sufficient power, the corresponding wave-... 

For calculating bound-state energies and wave functions, A 0 and the filter becomes equivalent to the spectral density operator S Ei — H) [208]. In the case of resonances, the Green s function in Eq. (33) selects the contributions from those complex poles whose real parts lie near Ei. In what follows we consider only the filter defined in Eq. (33). 

Therefore we are going to examine the critical behavior of the system defined by Hamiltonian (101) using the FSS method described in Section IV. That is, we are going to calculate the values of a and J for which a bound-state energy becomes absorbed or degenerate with a continuum. We define Jcn a) as the value of J for which the w-bound-state energy becomes equal to zero (the threshold energy is set at zero)... 

The time-dependent wave packet propagation can be employed to obtain bound state energies and bound state wavefunctions without the need to diagonalize the Hamiltonian matrix. The application of the method to bound state calculation is quite straightforward. If the Hamiltonian supports bound states 4> with eigenenergies Etn one can expand any given initial wave packet in this eigenbasis set,... 

Find the allowed bound-state energy levels for the system of Problem 2.21 by using a programmable calculator or computer to calculate the left side of (2.35) for e going from 0 to 1 in small steps. 

Schrodinger equation and solve for the bound-state energy levels. To obtain decay rates, we again use perturbation theory to calculate transition matrix elements between the bound-state levels. 

The Franck-Condon approximation is used to calculate the intensities. The bound state energies and wave functions are obtained by numerically solving the Schrodinger equation ... 

Similar calculations with consideration of the GP effect have also been reported [12]. A total of 24, 24, and 50 levels of Aj, A2, and E symmetries have been found below tbe dissociation threshold of the lower surface, —1.0560 eV. These are therefore genuine bound states the cone states lying above sucb a dissociation threshold are pseudobound states. The lowest levels of A, A2, and E symmetries are found to lie at —1.3475, —1.3438, and —1.3989eV, respectively. The notable feature is that the energy levels have been shifted due to the... 

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