We present in this letter a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach. We discuss the statistical properties of these states, by deducing the Q-and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

Assuming a symmetric matrix-valued potential that approaches constant endstates with a sufficient asymptotic rate, we relate the Maslov and Morse indices for Schrödinger operators on R. In particular, we show that with our choice of convention, the Morse index is precisely the negative of the Maslov index. Our analysis is motivated, in part, by applications to stability of nonlinear waves, for ...

This paper presents improved lower bounds for the total energy and the minimal inter-particle distance in minimal energy atom cluster problems with interactions given by a Morse potential. The methods use simple arguments and can be employed directly for Morse clusters, where the atom separation problem is difficult due to the finite energy at zero atom separation. The theoretical results are a...

Abstract. We prove a theorem about elliptic operators with symmetric potential functions, defined on a function space over a closed loop. The result is similar to a known result for a function space on an interval with Dirichlet boundary conditions. These theorems provide accurate numerical methods for finding the spectra of those operators over either type of function space. As an application,...

This study aims to apply a semi-classical approach using some analytically solvable potential functions accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. also at comparing accuracy within framework approximation. The performance approximation was investigated as function mass. In this approximation, nuclei w...