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(a) Consider two particles without spin that interact with a central potential V (r). Both particles are in the same state of orbital angular momentum and the corresponding quantum numbers are ji = j2 = 1. After performing the sum of angular moments, it is found that some of the states of the coupled base written in terms of the elements of the uncoupled base are: |2, 2) = |1, 1; 1, 1) 1 |2,0) = V6 (|1, 1; 1, –1) + 2|1, 1; 0, 0) + |1, 1; –1, 1)] %3D 1 |1, –1) = |1, 1;0, – 1) – |1, 1; – 1,0)] [|1, 1;0, –1) – |1, 1; –1,0)]

(a) Consider two particles without spin that interact with a central potential V (r). Both particles are in the same state of orbital angular momentum and the corresponding quantum numbers are ji = j2 = 1. After performing the sum of angular moments, it is found that some of the states of the coupled base written in terms of the elements of the uncoupled base are: |2, 2) = |1, 1; 1, 1) 1 |2,0) = V6 (|1, 1; 1, –1) + 2|1, 1; 0, 0) + |1, 1; –1, 1)] %3D 1 |1, –1) = |1, 1;0, – 1) – |1, 1; – 1,0)] [|1, 1;0, –1) – |1, 1; –1,0)]

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Adding angular moments: the wave function of the system 3 (a) Consider two particles without spin that interact with a central potential V (r). Both particles are in the same state of orbital angular momentum and the corresponding quantum numbers are j = j2 = 1. After performing the sum of angular moments, it is found that some of the states of the coupled base written in terms of the elements of the uncoupled base are: |2, 2) = |1, 1; 1, 1) 1 |2,0) : [1, 1; 1, -1) + 2|1, 1; 0, 0) + |1, 1; -1, 1)] 9/ |1, –1) = [[1, 1;0, -1) - |1, 1; –1,0)] V2 Write the corresponding wave functions in the spherical coordinate space, that is, explicitly write (ri, rlj, m). Hint: Remember that the solutions of the Schrodinger equation for any central potential are of the form Uk.i,m(r,0, ) = Rk.1(r)Yi,m(0, 4).
Transcribed Image Text:Adding angular moments: the wave function of the system 3 (a) Consider two particles without spin that interact with a central potential V (r). Both particles are in the same state of orbital angular momentum and the corresponding quantum numbers are j = j2 = 1. After performing the sum of angular moments, it is found that some of the states of the coupled base written in terms of the elements of the uncoupled base are: |2, 2) = |1, 1; 1, 1) 1 |2,0) : [1, 1; 1, -1) + 2|1, 1; 0, 0) + |1, 1; -1, 1)] 9/ |1, –1) = [[1, 1;0, -1) - |1, 1; –1,0)] V2 Write the corresponding wave functions in the spherical coordinate space, that is, explicitly write (ri, rlj, m). Hint: Remember that the solutions of the Schrodinger equation for any central potential are of the form Uk.i,m(r,0, ) = Rk.1(r)Yi,m(0, 4).
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