Application of the hypervirial theorem scheme to the potential -D/cosh^2(r/R)

The well known potential -D/cosh^2(r/R)is studied with the aim of obtaining approximate analytic expressions mainly for the energies of the excited states with l≠0. Use is made of the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of 'Oscillator-like' potentials,as previous studies have shown. The energy eigenvalues are calculated in the form of an expansion, the first terms of which, in many cases, yield very satisfactory results.

Analysis of the binding energies of the Λ- particle in hypernuclei with the RHVT approach and the Gauss potential

An analysis is carried out mainly of the ground state binding energies of the Λ-particle in hypernuclei with values of the core mass number AC between 15 and 207 (included) using, as far as possible, recent experimental data.Τhe renormalized (non- relativistic) quantum mechanical hypervirial theorem (RHVT) technique is employed in the form of s- power series expansions and a Gauss single particle potential for the motion of a Λ- particle in hypernuclei is used. Not exact analytic solution is known for the Schrödinger eigenvalue problem in this case. Thus, the approximate analytic expressions (AAE) for the energy eigenvalues which are obtained with the RHVT approach and are quite useful as long as the involved dimensionless parameter s is sufficiently small, are compared only with the numerical solution. The potential parameters are determined by a least-squares fit in the framework of the rigid core model for the hypernuclei. A discussion is also made regarding the determination of the renormalization parameter χ.

GENERALIZED HYPERVIRIAL THEOREM FOR THE D DIMENSIONAL SINGLE-PARTICLE SYSTEM AND ITS APPLICATIONS

By using the Hamiltonian identity, we present a generalized hypervirial theorem for the D dimensional single-particle system with arbitrary potential. It is shown that this generalized hypervirial theorem is powerful in deriving the Blanchard's and Kramers' recurrence relations among the matrix elements. We apply those recurrence relations to some physical systems, exactly solvable and unsolvable, such as the pseudoharmonic oscillator, the Morse, the modified Pöschl-Teller, the Lennard-Jones, the Buckingham and the Yukawa potentials. The Blanchard's and Kramers' recurrence relations in two dimensions are also briefly mentioned.