Positive Energy Bound States

Abstract

Positive energy bound states (PEBS) are introduced through a brief historical background. Few examples, including cases with partial waves higher than the 0th order, are then demonstrated. Related problems, such as the modification of Levinson's theorem, PEBS with perturbations and the interpretation of PEBS have been reviewed. The present status of the subject is then discussed.

The Use of Some Important Integrals in Physics

“…from the previous calculations in this section ,It is clear how important our integrals are; details can be referred to references [3], [4], [5].…”

“…AN ILLUSTRATIVE APPLICATION The integrals, shown above, have their importance and usefulness in many problems in physics, especially in studying positive energy bound states(PEBS) [2], [3[,[4], [5] . Below we give an example, to show how important these integrals in solving some physical problems.…”

“…Below we give an example, to show how important these integrals in solving some physical problems. The question of PEBS is fundamental in theoretical nuclear physics and the subject has been of interest quite for a long time [5]; where it is found that for a certain class of non-local potentials ,the s-wave Schrodinger equation…”

“…Has a solution ᴪ( , ) ,such that ᴪ( , ) → 0 → ∞; at the energy = . Such a solution is called a positive energy bound state; a PEBS is interpreted as a zero-width resonance .The existence of PEBS or scattering phase shifts at PEBS ,for certain conditions, have been discussed and given, leading to the need for a new interpretation [5]. Now ,generalizing to cases with any −partial wave ( = 0,1,2,3, .. ),we see that the − Schrodinger equation ,with a nonlocal seperable potential ( , ) = ( ) ( , ) (24) , is given as…”