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The asymptotic iteration method for the eigenenergies of the complex potential

The asymptotic iteration method for the eigenenergies of the complex potential. A. J. Sous Al-Quds Open University Nablus. Many authors studied several complex potentials, and showed that the energy eigenvalues of the Schrödinger equation. are real.

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The asymptotic iteration method for the eigenenergies of the complex potential

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  1. The asymptotic iteration method for the eigenenergies of the complex potential A. J. Sous Al-Quds Open University Nablus

  2. Many authors studied several complex potentials, and showed that the energy eigenvalues of the Schrödinger equation are real

  3. As a first potential model, Bender and Boettcher applied theRunge-Kutta technique and the WKB approximation in the complex plane to obtain the discrete energy eigenvalues of the PT -symmetric non-Hermitian potential. And showed that the discrete spectrum generated by the potential (2) should be real

  4. As second potential model, Delabaere and Trinh applied asymptotic method, while Handy applied the eigenvalue moment method (EMM), and multiscale reference function (MRF) approach to calculate the eigenenergies of the potential

  5. As a third potential model, Delabaere, and Pham applied the WKB approximation method and WKB exact method to generate values for discrete eigenenergies states of the potential While Handy used the EMM to generate the low-lying bound states for the potential (4)

  6. In this study, we will combine the above three potentials in a single new complex potential, for which the eigenvalues of each one of the three potentials above can be calculated through new single complex potential for each one.

  7. To see this, we introduce the new complex potential as: where, at least one of the parameters must equal zero, and only one of them must equal one for each case .

  8. Therefore, in order to apply the AIM we will assume that Where is an adjustable parameter introduced to improve the rate of convergence of the AIM.

  9. Substitution the wave function (6) in to Schrödinger equation (1) gives the following homogeneous linear second-order differential equation

  10. Where In order to find the general solution to equation (7), we will apply the AIM. Thus, if we differentiate (7) we obtain

  11. Where In some suitable large iterations one can numerically determine the eigenenergies from the roots of the equation

  12. Where

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