Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach

Altug Arda; Ramazan Sever

Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach

Mathematical Physics 2012-06-29 v1 math.MP Quantum Physics

Authors: Altug Arda , Ramazan Sever

Abstract

We intend to realize the step-up and step-down operators of the potential $V(x)=V_{1}e^{2\beta x}+V_{2}e^{\beta x}$ . It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential ( $\beta \rightarrow -\beta$ ).

Keywords

Morse-like potential ladder operators Laplace transform SU(2) group Lie algebra exact solutions eigenvalues

Cite

@article{arxiv.1205.3903,
  title  = {Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach},
  author = {Altug Arda and Ramazan Sever},
  journal= {arXiv preprint arXiv:1205.3903},
  year   = {2012}
}

Comments

8 pages

Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach

Abstract

Keywords

Cite

Comments

Related papers