# 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 1Orbital angular momentum eigenstatesUse 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,⟨L**

_{z}⟩?

Answer: 0.015

**Question 2What is the probability of measuring L _{z} and obtain 0?**

Answer: 0.00026

**Question 3What is the probability of measuring L _{z} and obtain 2ℏ?**

Answer: 0.52

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

**Question 4Angular momentum eigenstatesUse 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, Y**

_{lm}.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.

Answer:

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

**Question 5Angular momentum eigenstatesWhat is the expectation value of L**

^{^2}?Give your answer in unit of ℏ

^{2}.

Answer: 2

**Question 6Angular momentum eigenstatesWhat is the probability of measuring m=0?**

Answer: 0.67

**Question 7Angular momentum eigenstatesWhat is the probability of measuring m=+1?**

Answer: 0.17

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

**Question 8Hydrogen atomUse 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(√10ψ**

_{100}+3ψ

_{211}+4ψ

_{210}−ψ

_{21-1})where ψ

_{nlm}is the energy eigenfunction of hydrogen atom.What is the expectation value of energy?Give the answer in unit of Ry, Rydberg constant.

Answer: -0.46

**Question 9What is the expectation value of L ^{^2}?Give the answer in unit of ℏ^{2}.**

Answer: 1.4

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

Answer:

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

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