Complex Energy Eigenvalues Research Articles

New structure in the energy spectrum of reggeon quantum mechanics with quartic couplings

We find general that the energy spectrum of the reggeon hamiltonian with cubic plus quartic interactions at D=0 is more complicated than previously assumed. We observe the phenomenon of “ground state oscillation”, which suggests, for D ≠ 0, the existence of multiple phases. We find that for certain values of the parameters of the theory complex energy eigenvalues occur. We also find complicated level crossings among higher eigenvalues as the quartic coupling strength is increased.

On the complex energy eigenvalue theory of alpha decay

We have developed a method to compute alpha decay widths in the theoretical frame of the complex energy eigenvalue. We apply it to 102 alpha decays of even-even nuclei. The theoretical values reproduce reasonably well the experimental results and they also show that there is a structure which depends on the orbital angular momentum of decay.

Possibility of complex eigenvalues in approximate solutions of the homogeneus Faddeev equations and their implication for the general n-body case

It is shown that use of approximations similar to those encountered in atomic, molecular and nuclear scattering and also in shell model (bound state) calculations may give rise to complex energy eigenvalues for the Faddeev 3-body equations. This is in contradistinction to results based on exact solutions or on use of separable approximations. Some implications for the general many-body case are noted.

Resonant states and their uses

The paper shows, for a simple model, how the wave functions belonging to complex energy eigenvalues (resonance states) can be regarded as part of a complete set of states, containing also bound states and a continuum of (generally complex) wave functions. This forms the basis of an expansion, which is used to describe inelastic scattering in the plane-wave Born approximation, taking the same simple model for the target.

A theory of the broadening of the infrared absorption spectra of hydrogen-bonded species. I

A theory of the intramolecular contributions to the broadening of thev(XH) absorption bands of hydrogen-bonded species is proposed, which is able to describe both vibrational predissociation and the formation of sum and difference bands. A formal method is developed for finding the wavefunctions and complex energy eigenvalues of quasi-stationary excited vibrational states of a linear triatomic system with realistic interactions. The theory is applied to the Me2O.HCl system. It is found that predissociation broadening is negligible. The calculation of combination band intensities, and of the spread in energy of terms within such bands, will be reported in a subsequent paper.

Lee model with complex energy eigenvalues

The Lee model with fixed point particles is investigated when complex energy eigenvalues appear in the subspace (V, N+θ). It is proved that in general such a model has no physical interpretation, at least in the usual framework. Indeed a problem in the subspace (2V+θ, V+N+2θ, 2N+3θ) is considered, and it is shown that expressions which are usually interpreted as probabilities become negative. Such difficulties do not appear in simpler problems.

Discrete States for Singular Potential Problems

The solutions of the quantum mechanical wave equations for singular potentials are re-examined. It is shown that a set of orthonormal wave functions with complex energy eigenvalues (E/sub n/ = W/sub n/ plus or minus 1/2i GAMMA / sub n/) is obtained if certain natu ral analyticity requirements are imposed on the form of the potentials. In general, the result is interpreted in the following way: W/sub n/ is the most probable position of the energy level for various types of cutoff and GAMMA /sub n/ is a measure of the probable error. (auth)