Solution of Radial Schrödinger Equation with Yukawa Potential Using Bethe Ansatz Method
M. Mohammadi Sabet
Department of Physics, Faculty of Science, Ilam University, Ilam, Iran
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The quasi-exact Bethe ansatz method has been examined for solving the radial Schrödinger equation with the Yukawa potential as an important central interaction for computing bound states of neutral atoms. The method, in spite of its simplicity with respect to other methods, leads to the ground state and low excited states of the radial Schrödinger equation with a good accuracy. It is found that the results are generally in agreement with the results of others and, therefore, this method can be used for solving the Schrödinger equation instead of other numerical and analytical methods. It was also found that the energy eigenvalues reach that of the Coulomb potential in the limit of zero screening parameter. The method has been briefly generalized to arbitrary dimension for the Yukawa potential inspiring the 3-dimensional trail wave function.

DOI:10.12693/APhysPolA.140.97
topics: Yukawa potential, Bethe ansatz method, quasi-exact solution, Schrödinger equation