that ( L x 2 + L y 2 ) 1 / 2 = [ l l + 1 - m l 2 ] 1 / 2 ћ if the orbital angular momentum L → is measured along the z-axis to obtains a value L z . And that this is the most that can be said about the two components of the orbital angular momentum.

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Answer 1

Question

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

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Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2

Notation matters when working with vectors! In particular, it is important to distinguish between the vector itself (A) and its magnitude (A). Illustrate in four separate sketches that each of the following statements is possible: a) both R = A + B and R=A+B are correct b) R = A + B is correct, but R=A+B is incorrect c) R = A + B is incorrect, but R=A+B is correct d) both R = A + B and R=A+B are incorrect

Answer 2

Question

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Answer 6

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Answer 7

Chapter 40, Problem 11P

To determine

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 40 - Prob. 1Q Ch. 40 - Prob. 2Q Ch. 40 - Prob. 3Q Ch. 40 - Prob. 4Q Ch. 40 - Prob. 5Q Ch. 40 - Prob. 6Q Ch. 40 - Prob. 7Q Ch. 40 - Figure 40-22 shows three points at which a spin-up...Ch. 40 - Prob. 9Q Ch. 40 - Prob. 10Q

that ( L x 2 + L y 2 ) 1 / 2 = [ l l + 1 - m l 2 ] 1 / 2 ћ if the orbital angular momentum L → is measured along the z-axis to obtains a value L z . And that this is the most that can be said about the two components of the orbital angular momentum.

Solution Summary: The author explains that the orbital angular momentum is measured along the z-axis to obtain a value, and that this is the most that can be said about the two components.

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.

Want to see the full answer?

Chapter 40 Solutions

that ( L x 2 + L y 2 ) 1 / 2 = [ l l + 1 - m l 2 ] 1 / 2 ћ if the orbital angular momentum L → is measured along the z-axis to obtains a value L z . And that this is the most that can be said about the two components of the orbital angular momentum.

Solution Summary: The author explains that the orbital angular momentum is measured along the z-axis to obtain a value, and that this is the most that can be said about the two components.

To show: that (Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ if the orbital angular momentum L→ is measured along the z-axis to obtains a value Lz. And that this is the most that can be said about the two components of the orbital angular momentum.

Want to see the full answer?

Chapter 40 Solutions

To show:

that

(Lx2+ Ly2)1/2= [ll+1-ml2 ]1/2ћ

if the orbital angular momentum L→ is measured along the z-axis to obtains a value L_z.

And that this is the most that can be said about the two components of the orbital angular momentum.