Exact solutions for a Hamiltonian with the Morse potential and the Dirac delta shell interactions

Abstract

We construct a method to obtain s-wave bound states of the Schrödinger equation for the Morse potential together with a finite number of the Dirac delta interactions. We derive an eigenvalue equation for energies and calculate the ground state energy and the frequencies for the transitions between the low-lying energy levels for one delta interaction case. We analyse the condition for the number of bound states for given parameters of the potential. For a simple description of the interaction between an encapsulated H₂ molecule and C₆₀ cage, we utilise our method for representing the interaction potential by a Dirac delta interaction. We also perform the stabilisation energy calculation for this system. Interatomic interactions that are described by a Morse potential together with local deformations can be investigated by using our model.

Keywords:

• Morse potential
• Dirac delta interactions
• bound states
• endohedral C₆₀

Acknowledgements

This work has been supported by Turkish Academy of Sciences, in the framework of the Young Scientist Award Program (ED-TÜBA-GEBIP-2001-1-4).