Four-Parameter Potential Function with Negative Energy Bound States

Mohamed Améziane Sadoun, Redouane Zamoum, Abdellah Touati

In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help of an appropriate approximation to evaluate the centrifugal term, the energy spectrum and the normalized wave functions of the bound states are derived from the poles of Green's function and its residues. The partition function and other thermodynamic properties were obtained using the compact form of the energy equation.

Chun‐Sheng Jia, Yun Li, Yu Wei Sun +2 more

I. B. Okon, Oyebola O. Popoola, Cecilia N. Isonguyo

In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method.We also obtained the energy eigen value and its associated total wave function .This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential.Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter.The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant).The graph in figure (1) shows the different energy levels for a particular quantum number.

A. Ronveaux

D. K. Gridnev

We consider a system of N pairwise interacting particles described by the Hamiltonian H, where σess(H) = [0, ∞) and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs and obey certain restrictions regarding the fall off. It is proved that if N ⩾ 4 and none of the Hamiltonians corresponding to the subsystems containing N − 2 or less particles has an eigenvalue equal to zero then H has a finite number of negative energy bound states. This result provides a positive proof to a long-standing conjecture of Amado and Greenwood stating that four bosons with an empty negative continuous spectrum have at most a finite number of negative energy bound states. Additionally, we give a short proof to the theorem of Vugal'ter and Zhislin on the finiteness of the discrete spectrum and pose a conjecture regarding the existence of the “true” four-body Efimov effect.

James H. Goble, John S. Winn