%0 Journal Article
%T Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension
%A Hippolyte Nyengeri
%A Ren¨¦ Simbizi
%A Audace Girukwishaka
%A R¨¦novat Nizigiyimana
%A Eug¨¨ne Ndenzako
%J Open Access Library Journal
%V 5
%N 7
%P 1-14
%@ 2333-9721
%D 2018
%I Open Access Library
%R 10.4236/oalib.1104728
%X <div style="text-align:justify;">
	<span style="line-height:1.5;">The
Schrodinger equation (SE) for a certain class of symmetric hyperbolic
potentials is solved with the aid of the Frobenius method (FM). The bound state
energies are given as zeros of a calculable function. The calculated bound
state energies are successively substituted into the recurrence relations for
the expanding coefficients of the Frobenius series representing even and odd
solutions in order to obtain wave functions associated with even and odd bound
states. As illustrative examples, we consider the hyperbolic Poschl-Teller
potential (HPTP) which is an exactly solvable potential, the Manning potential
(MP) and</span><span style="line-height:1.5;"> a model of the Gaussian potential well (GPW). In each example, the
bound state energies obtained by means of the FM are presented and compared
with the exact results or the literature ones. In the case of the HPTP, we also
make a comparison between exact bound state wave functions and the
eigenfunctions obtained by means of the present approach. We find that our
results are in good agreement with those given by other methods considered in
this work, and that our class of potentials can be a perfect candidate to model
the GPW.</span> 
</div>
%K Schrodinger Equation
%K Hyperbolic Potential
%K Frobenius Method
%K Wave  Functions
%K Bound States
%U http://www.oalib.com/paper/5297685