- #1
carllacan
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Homework Statement
The atomic nucleus of Deuterium is a bound state of two nucleons.
Through a change of coordinates we can transform the situation into a central force problem with a potential described by -V0 for r > R and 0 for r < R.
In the ground state of this nucleus the angular momentum number is l=0.
Find the binding energy of the nucleons.
Homework Equations
The radial equation: http://en.wikipedia.org/wiki/Partic...c_potential#Derivation_of_the_radial_equation
The Attempt at a Solution
I have two (second degree) radial equations (inside and outside of R) with different E, both with l = 0. I also have two conditions at r = R, where the two solutions and their derivatives have to be equal. I also have the normalization condition.
That makes three constraints for four constants (plus the energy), so I can't solve it.
I've tried adding the condition that ψ(0) = 0, because the nucleons can't be in the same place. This would allow me to find the energy inside R, which I think would be the end of the problem (since I am just asked to find the binding energy), but I'm not sure it is right, especially because doing it like this I get a solution with no dependence of V0.
Can you tell me how to continue from here?
Thank you for your time.