Consider a composite state of an electron with total angular momentum j1 = 1/2 and a proton with angular momentum j2 = 3/2. Find all the eigenstates of |j1,j2;j,m⟩ as the linear combination of product states of angular momentum of electron and proton |j1,j2;m1,m2⟩. Give the values of Clebsch-Gordon coefficients you get from here. If the system is found in state |j1 = 1/2,j2 = 3/2;j = 1,m = −1⟩, what is the probability that j1z = −1/2 and what is the probability that j1z = 1/2

Consider a composite state of an electron with total angular momentum j1 = 1/2 and a proton with angular momentum j2 = 3/2. Find all the eigenstates of |j1,j2;j,m⟩ as the linear combination of product states of angular momentum of electron and proton |j1,j2;m1,m2⟩. Give the values of Clebsch-Gordon coefficients you get from here. If the system is found in state |j1 = 1/2,j2 = 3/2;j = 1,m = −1⟩, what is the probability that j1z = −1/2 and what is the probability that j1z = 1/2

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Question

Consider a composite state of an electron with total angular momentum j₁= 1/2 and a proton with angular momentum j₂= 3/2. Find all the eigenstates of |j₁,j₂;j,m⟩ as the linear combination of product states of angular momentum of electron and proton |j₁,j₂;m₁,m₂⟩. Give the values of Clebsch-Gordon coefficients you get from here. If the system is found in state |j₁= 1/2,j₂= 3/2;j = 1,m = −1⟩, what is the probability that j_1z= −1/2 and what is the probability that j_1z= 1/2

Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.

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