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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

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

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