On the analytical solutions of the quasi-exactly solvable Razavy type potential V(x) = Vo (sinh**4(x)-k sinh**2(x) )
arXiv: High Energy Physics - Theory(2018)
Abstract
In order to show how stringent the restrictions posed on analytical solutions of quasi-exactly solvable potentials are, we construct analytical solutions for the Razavy type potential V(x) = Vo (sinh**4(x)-k sinh**2(x) ) based on the polynomial solutions of the related Confluent Heun Equation, where the free parameter k allows to tune energy eigenvalues, a desirable feature in different theories. However, we show that with the described method, the energy eigenvalues found diverge when k (goes to) -1, a feature caused solely by the procedure.
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