Solved: Griffiths Prob 5.41 | Angular Momentum

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In summary, The question refers to a problem in Griffiths' E and M book, and the asker is trying to find the total change in angular momentum. They are wondering if they should assume that the initial velocity is perpendicular to the B-field and if the particle's motion should be in the plane of the page. There have been suggestions from others that the particle's motion should be in the plane of the page for the problem to be interesting. However, the problem does not explicitly state this.
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ehrenfest
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[SOLVED] Griffiths Problem 5.41

Homework Statement


This question refers to Griffiths E and M book.

http://www.phys.unsw.edu.au/~gary/PHYS2050_Tut_5.pdf [Broken]

Homework Equations


The Attempt at a Solution


Am I supposed to assume that the initial velocity is perpendicular to the B-field i.e. in the plane of the page?

I am trying to find the total change in angular momentum and the integral just seems evaluatable unless I do that.
 
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  • #2
Which problem?
 
  • #3
5.41
 
  • #4
anyone?
 
  • #5
I think you'd get a few more responses if you copy/pasted the question - people are lazy.

I think you're supposed to do it with the particle traveling the in plane of the page - it wouldn't really be too interesting if the particle's motion was parallel to the magnetic field, since the force would be zero due to the Lorentz force law.

The problem doesn't explicitly say that, though... Bad Griffiths!

-Nathan Goldbaum
 

1. What is the problem being solved in Griffiths Prob 5.41?

The problem being solved is related to angular momentum in quantum mechanics. Specifically, it involves finding the expectation value of the z-component of the angular momentum for a particle in a spherically symmetric potential.

2. How is the problem approached in Griffiths Prob 5.41?

The problem is approached using the Schrödinger equation and the commutation relations for angular momentum operators. The solution involves finding the eigenvalues and eigenfunctions of the angular momentum operator and then using them to calculate the expectation value.

3. What are the key concepts involved in solving Griffiths Prob 5.41?

The key concepts involved include angular momentum, quantum mechanics, eigenvalues and eigenfunctions, commutation relations, and expectation values. It also requires knowledge of spherical harmonics and the radial wave function.

4. What is the significance of solving Griffiths Prob 5.41?

Solving this problem helps us understand the behavior of particles in spherically symmetric potentials and how angular momentum is quantized in quantum mechanics. It also demonstrates the usefulness of the commutation relations in solving quantum mechanical problems.

5. Are there any real-world applications of Griffiths Prob 5.41?

Yes, there are real-world applications of this problem in fields such as atomic and molecular physics, where the behavior of particles in spherically symmetric potentials is important. Understanding angular momentum in quantum mechanics also has implications in solid state physics and nuclear physics.

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