# 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 1SpinorUse 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.**

Answer: a^2

**Question 2SpinorWhen 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.**

Answer: (a+b)^2/2

**Question 3SpinorWhen 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.**

Answer:

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

**Question 4Spin 1/2 systemUse 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.

Answer: 1/sqrt(2)

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

**Question 5Spin 1/2 systemEnter 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.**

Answer: 1/sqrt(2)

**Question 6Spin 1/2 systemWe 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.**

Answer: -1/sqrt(2)*i

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

**Question 7Spin 1/2 systemEnter 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.**

Answer: 1/sqrt(2)*i

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

Answer: 0.000163

**Question 9Spin 1/2 systemThis 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?**

Answer: 1.00003

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

**Question 10Spinor representationUse 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?

Answer: 0.3827

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

**Question 11Spinor representationWhat is the value of b?**

Answer: -0.9239

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

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