Explore BrainMass

Physics: Quantum Mechanics

The deuteron is a nucleus of "heavy hydrogen" consisting of one proton and one neutron. As a simple model for this nucleus, consider a single particle of mass m moving in a fixed spherically-symmetric potential V(r), defined by V(r)=-V0 for r<r0 and V(r)=0 for r>r0. This is called a spherical square-well potential. Assume that the particle is in a bound state with l=0.

a) Find the general solution R(r) to the radial Schrodinger equation for r<r0 and r>r0. Use the fact that the wave function must be finite at 0 and infinity to simplify the solution as much as possible. (You do not have to normalize the solutions)

b) The deuteron is only just bound; i.e., E is nearly equal to 0. Take m to be the proton mass, m=1.67x10^(-27) kg, and take r0 to be a typical nuclear radius, r0=1x10^(-15) m. Find the value of V0 (the depth of the potential well) in MeV (1 MeV = 1.6x10^(-13) J). (Hint: The continuity conditions at r0 must be used. The radial wave function R(r) and its derivative R'(r) must both be continuous at r0; this is equivalent to requiring that u(r) and u'(r) must both be continuous at r0, where u(r)=rR(r). The resulting equations cannot be solved exactly but can be used to derive the value for V0.)

Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is ...

Solution Summary

This solution provides a detailed, step by step explanation of the given physics problem.