(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 j₁ 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 12,0) [|1, 1; 1, -1) +2|1, 1; 0,0) + 1, 1; -1, 1)] /6 |1,−1) = √ [|1, 1;0, −1) − |1, 1; −1, 0)] = Write the corresponding wave functions in the spherical coordinate space, that is, explicitly write (ri,ralj, m). Hint: Remember that the solutions of the Schrodinger equation for any central potential are of the form kl,m (r,0,0) = Rk.1(r) Yim (0,0).
(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 j₁ 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 12,0) [|1, 1; 1, -1) +2|1, 1; 0,0) + 1, 1; -1, 1)] /6 |1,−1) = √ [|1, 1;0, −1) − |1, 1; −1, 0)] = Write the corresponding wave functions in the spherical coordinate space, that is, explicitly write (ri,ralj, m). Hint: Remember that the solutions of the Schrodinger equation for any central potential are of the form kl,m (r,0,0) = Rk.1(r) Yim (0,0).
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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 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) :
[|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 k.1,m(r, 0, 4) = Rk.1(r)Yı,m(0, 4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff758dc98-ba8f-44a7-9332-fa6cb562a169%2F732c8e53-48db-41f7-a937-01d99a4a2bff%2F9ii02ma_processed.jpeg&w=3840&q=75)
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 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) :
[|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 k.1,m(r, 0, 4) = Rk.1(r)Yı,m(0, 4).
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