I am studying the Pöschl-Teller potential in spherical coordinates and doing a change of variable is enough to put it in another sort of differential equation and thus, obtain the solution.

The point is: how can I find the eigenstates of this potential?

The second answer is: the eigenstates of the potential must be the same to any solutions? For example, the solution in terms of Heun function, hypergeometric function, etc.

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    $\begingroup$ I'm not sure I understand: the eigenstates are the solutions to the resulting Schrödinger equation. You make changes of variable to simplify the solution to the DE but the solutions are the solutions. $\endgroup$ – ZeroTheHero Jan 13 at 19:44
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    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ – Gert Jan 13 at 20:53

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