# Theory of Angular Momentum | Week 2

Course Name: Theory of Angular Momentum

Course Link: Theory of Angular Momentum

#### These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 1
Spinor
Use the following information for Questions 1-3:
An electron is in a state specified by spinor(ab​).
When z-component of spin is measured, what is the probability of measuring +ℏ/2​?
Express your answers in terms of a, b, imaginary unit i and reduced Planck’s constant hbar.

Question 2
Spinor
When x-component of spin is measured, what is the probability of measuring +ℏ/2​?
Express your answers in terms of a, b, imaginary unit i and reduced Planck’s constant hbar.

Question 3
Spinor
When y-component of spin is measured, what is the probability of measuring +ℏ/2?
Express your answers in terms of a, b, imaginary unit i and reduced Planck’s constant hbar.

These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 4
Spin 1/2 system
Use this information to answer Question 4-9:
An electron was found in the eigenstate of S^x​ with eigenvalue of +ℏ/2​.
Using the two eigenkets of S^z​ as the basis, express the spin state in the two-component spinor representation, (a b​).
Enter the expression for the first element a in terms of imaginary unit, i, and reduced Planck’s constant hbar. Note that your expression may not include all of these parameters.

These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 5
Spin 1/2 system
Enter the expression for the second element b in terms of imaginary unit, i, and reduced Planck’s constant hbar. Note that your expression may not include all of these parameters.

Question 6
Spin 1/2 system
We now rotate the state by 180 degrees about z -axis. Express the resulting state in spinor, (c d​).
Enter the expression for the first element c in terms of imaginary unit, i, and reduced Planck’s constant hbar. Note that your expression may not include all of these parameters.

These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 7
Spin 1/2 system
Enter the expression for the second element d in terms of imaginary unit, i, and reduced Planck’s constant hbar. Note that your expression may not include all of these parameters.

Question 8
Spin 1/2 system
Suppose we measured the x-component of spin again after the rotation. What is the probability of measuring +ℏ/2?

Question 9
Spin 1/2 system
This time, we rotate the original state given in Question 4 by 360 degrees about z-axis.
What is the probability of measuring +ℏ2+2ℏ​ for the x-component of spin after the rotation?

These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 10
Spinor representation
Use the following information for Questions 10-11:
n^ is the unit vector in the yz plane that bisect the angle between y and z axes. That is, n^ makes a 45 degree angle with respect to both y and z axes.
Write down the 2×2 matrix representation for σ⋅n^ and find the spinor for the eigenvector of σ⋅n^ with eigenvalue −1. Here σ is a vector whose x-, y-, z-components are given by the Pauli’s spin matrices.
Express your answer in a two-dimensional vector form, (a ib​), where a and b are real numbers and a>b. What is the value of a?

These are answers of Theory of Angular Momentum Coursera Week 2 Quiz

Question 11
Spinor representation
What is the value of b?