The first and second Pöschl-Teller differential equations are given by
![y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0](/images/equations/Poeschl-TellerDifferentialEquations/NumberedEquation1.svg) |
and
![y^('')-{a^2[(kappa(kappa-1))/(sinh^2(ax))+(lambda(lambda-1))/(cosh^2(ax))]-b^2}y=0](/images/equations/Poeschl-TellerDifferentialEquations/NumberedEquation2.svg) |
respectively.
Pöschl-Teller Differential Equations
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References
Barut, A. O.; Inomata, A.; and Wilson, R. "Algebraic Treatment of Second Pöschl-Teller, Morse-Rosen, and Eckart Equations." J. Phys. A: Math. Gen. 20, 4083-4096, 1987.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 126, 1997.Referenced on Wolfram|Alpha
Pöschl-Teller Differential EquationsCite this as:
Weisstein, Eric W. "Pöschl-Teller Differential Equations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Poeschl-TellerDifferentialEquations.html