# exponential potential in physics

given the differential equation

$$-\hbar^{2}D^{2}y(x)+ae^{bx}y(x)=E_{n}y(x)$$

here $D=d/dx$ derivative

are there examples in physics where this potential appears ??, i know how to solve it but i do not know pratical examples where the exponential potential appears

the solution is given by

http://www.wolframalpha.com/input/?i=-y%27%27%28x%29%2Baexp%28bx%29y%28x%29%3Dcy%28x%29

• a particle falls down from a hill? – user26143 Aug 1 '13 at 21:27
• How about a Yukawa-type potential? – Wouter Aug 1 '13 at 21:50