# 1D Time independent Schrodinger eq. with limit

The one dimensional Schrodinger equation for an exponential potential

$$-{\hbar^2\over 2m} \frac{d^2\psi}{dx^2}+-\alpha\frac{e^{-\vert x\vert\over\epsilon}}{2\epsilon}\psi=E\psi$$

I am interested in solving this equation with the limit as $$\epsilon \rightarrow 0$$. My goal is to check the equivelance between the dirac delta function explicit bound state solution with the above representation.

is it reasonable to solve this equation and then dealing with the limit, and how?

• So... what's the question here? – Emilio Pisanty Mar 21 at 12:38
• is it reasonable to solve this equation and then dealing with the limit, and how? – R. Usef Mar 21 at 12:39
• I don’t think this potential has an analytical solution... – ZeroTheHero Mar 21 at 13:01
• Do we even know what the $\lim_{\epsilon \to 0}\frac{\exp{-\vert x\vert\over\epsilon}}{2\epsilon}$ is? – Gert Mar 21 at 14:50
• @Gert pretty sure it's a Dirac delta. – Javier Mar 21 at 15:24