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**Given a spherically symmetric attractive potential of the form V(r) = -V * e^(-r/a)**

To solve the schroedinger equation and obtain the quantization condition for the energy eigenvalues.

Hint : - Use the Substitution x = e ^ (-r/2a)

To solve the schroedinger equation and obtain the quantization condition for the energy eigenvalues.

Hint : - Use the Substitution x = e ^ (-r/2a)

I did the usual separation of variables psi = R * spherical harmonics

Also i substituted R = U/r and got the radial differential equation in U.

But now, I am stuck.. I know the asymptotic behavior of U. U tends to 0 as r goes to 0. As r tends to infinity, for bound state U will go as e ^ (-kr)

But i dont know what to do next... pls help.

thanks.

I did the usual separation of variables psi = R * spherical harmonics

Also i substituted R = U/r and got the radial differential equation in U.

But now, I am stuck.. I know the asymptotic behavior of U. U tends to 0 as r goes to 0. As r tends to infinity, for bound state U will go as e ^ (-kr)

But i dont know what to do next... pls help.

thanks.