# Griffiths Example 3.8: Justifications for Claims

• ehrenfest
In summary, the conversation discusses Example 3.8 in Griffiths' E and M book, where he makes two claims without justification. These claims are that V=0 in the equatorial plane and V \to -E_0 r \cos{\theta} for r >>R. The justification for this is that when converting from cartesian to spherical coordinates, z = r \cos{\theta}. Additionally, the uncharged metal sphere is assumed to have been grounded beforehand, leading to the conclusion that V=0 in the equatorial plane.
ehrenfest
[SOLVED] Griffiths Example 3.8

## Homework Statement

In Example 3.8, Griffiths makes two claims without justification that I want justification for. First, he says that V=0 in the equatorial plane (I assume this means that x-y plane). Second, he says that $$V \to -E_0 r \cos{\theta}$$ for $$r >>R$$. Where does the cosine come from?

ehrenfest said:

## Homework Statement

In Example 3.8, Griffiths makes two claims without justification that I want justification for. First, he says that V=0 in the equatorial plane (I assume this means that x-y plane). Second, he says that $$V \to -E_0 r \cos{\theta}$$ for $$r >>R$$. Where does the cosine come from?

The problem is originally defined in cartesian coordinates. Now that we are using the Legendre Polynomials it has to be in spherical coordinates.

Orginally:
$$V \to -E_0 z$$
goes to
$$V \to -E_0 r \cos{\theta}$$
since
$$z = r \cos{\theta}$$

And how do you know V=0 all over th equatorial plane?

It is an uncharged metal sphere, so we basically assume it was grounded beforehand

I see. Thanks.

## 1. What is Griffiths Example 3.8?

Griffiths Example 3.8 is a thought experiment presented in the textbook "Introduction to Quantum Mechanics" by David J. Griffiths. It involves a hypothetical scenario where a particle is trapped in an infinite square well potential and subjected to a small perturbation.

## 2. What is the purpose of Griffiths Example 3.8?

The purpose of Griffiths Example 3.8 is to illustrate the concept of perturbation theory in quantum mechanics. It also serves as an example of how physical claims can be justified mathematically using theoretical tools.

## 3. What are the justifications for claims made in Griffiths Example 3.8?

The justifications for claims made in Griffiths Example 3.8 include the application of perturbation theory, the use of mathematical proofs, and comparison to known physical principles and experimental results.

## 4. How does Griffiths Example 3.8 relate to real-world applications?

Griffiths Example 3.8 may not have direct real-world applications, but the principles and techniques used in the thought experiment are commonly applied in various fields of physics, such as quantum mechanics, solid state physics, and atomic physics.

## 5. Can the results of Griffiths Example 3.8 be generalized to other physical systems?

Yes, the results of Griffiths Example 3.8 can be generalized to other physical systems as long as they can be described by a similar mathematical model. However, the specific values and parameters may differ depending on the system being studied.

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