# Theory of Angular Momentum | Week 1

Course Name: Theory of Angular Momentum

Course Link: Theory of Angular Momentum

#### These are answers of Theory of Angular Momentum Coursera Week 1 Quiz

Question 1
Orbital angular momentum eigenstates
Use this information for Questions 1-3:
A particle in a central potential V(r) has a wavefunction of, ψ=f(r,θ)sin2ϕ where $\phi$ is the azimuthal angle in the spherical polar coordinate system. Also, this wavefunction ψ is properly normalized, i.e. ⟨ψ∣ψ⟩=1.
What is the expectation value of z-component of orbital angular momentum,⟨Lz⟩?

Question 2
What is the probability of measuring Lz and obtain 0?

Question 3
What is the probability of measuring Lz and obtain 2ℏ?

These are answers of Theory of Angular Momentum Coursera Week 1 Quiz

Question 4
Angular momentum eigenstates
Use this information for Questions 4-7:
A particle in a central potential V(r) has a wavefunction of the form, ψ=(x+y+2z)f(r)
Also, this wavefunction ψ is properly normalized, i.e. ⟨ψ∣ψ⟩=1.
Rewrite the wavefunction in terms of spherical harmonics, Ylm.
In your answer, enter spherical harmonics simply as Ylm without subscripting. Also, use Ylm for all zero or positive values of m and Zlm for negative values of m. For example, enter Y21 for l=2 and m=1 and enter Z11 for l=1 and m=−1. Finally, enter the radial function f(r) simply as f.

These are answers of Theory of Angular Momentum Coursera Week 1 Quiz

Question 5
Angular momentum eigenstates
What is the expectation value of L^2?

Question 6
Angular momentum eigenstates
What is the probability of measuring m=0?

Question 7
Angular momentum eigenstates
What is the probability of measuring m=+1?

These are answers of Theory of Angular Momentum Coursera Week 1 Quiz

Question 8
Hydrogen atom
Use this information for Questions 8-10:
Suppose the electron in a hydrogen atom is in a state described by the following wavefunction,)
ϕ= 1/6(√10ψ100​+3ψ211+4ψ210−ψ21-1​)
where ψnlm is the energy eigenfunction of hydrogen atom.
What is the expectation value of energy?
Give the answer in unit of Ry, Rydberg constant.

Question 9
What is the expectation value of L^2?
Give the answer in unit of ℏ2.

Question 10
What is the expectation value of L^z?
Give the answer in unit of ℏ.