Trying to see how these are equivalent

  • Thread starter hideelo
  • Start date
  • Tags
    Equivalent
In summary, the conversation is about a user working on the derivation of the angular momentum squared operator in quantum mechanics and needing help with a specific step. They posted their question in a mathematical forum and another user suggested using the product rule to simplify the equation. The user thanks them for the suggestion.
  • #1
hideelo
91
15
I am working on the derivation of the angular momentum squared operator (in quantum mech.) and there is one step that I don't see how it works. I'm not sure that this is the right place to post it, but since this is a strictly mathematical question, I figured I would post it here. The equivalence is as follows:

(cotθ)(∂/∂θ) + (∂/∂θ)2 = (cscθ)(∂/∂θ)[(sinθ)(∂/∂θ)]

I don't see how to go from one to the other
 
Physics news on Phys.org
  • #2
hideelo said:
I am working on the derivation of the angular momentum squared operator (in quantum mech.) and there is one step that I don't see how it works. I'm not sure that this is the right place to post it, but since this is a strictly mathematical question, I figured I would post it here. The equivalence is as follows:

(cotθ)(∂/∂θ) + (∂/∂θ)2 = (cscθ)(∂/∂θ)[(sinθ)(∂/∂θ)]

I don't see how to go from one to the other

Start on the right side, and take the derivative of (sinθ * (∂/∂θ)), using the product rule. This simplifies to what you have on the left side without too much effort.
 
  • Like
Likes 1 person
  • #3
Thanks :-) I don't know why I didnt try that
 

1. How do you determine if two things are equivalent in science?

In science, two things are considered equivalent if they have the same value, function, or effect. This can be determined through various experimental methods, statistical analysis, and observations.

2. Why is it important to establish equivalence in scientific research?

Establishing equivalence is crucial in scientific research because it allows for accurate and reliable comparisons between different variables or treatments. It also helps to eliminate bias and ensure the validity of the results.

3. What is the difference between equivalence and equality in science?

Equivalence refers to two things having the same value or effect, while equality refers to two things being exactly the same. In science, equivalence is often used to compare different variables or treatments, while equality is more commonly used in mathematical equations.

4. Can you give an example of how equivalence is tested in scientific experiments?

One example of testing equivalence in a scientific experiment is conducting a randomized controlled trial. In this type of study, participants are randomly assigned to different treatments or groups, and their outcomes are compared to determine if there is equivalence between the treatments.

5. How do you ensure that the results of a study are truly equivalent?

To ensure the results of a study are truly equivalent, scientists use various methods such as randomization, blinding, and controlling for confounding variables. Additionally, repeating the experiment multiple times and obtaining consistent results can also indicate equivalence.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
3
Views
962
  • Classical Physics
Replies
4
Views
794
Replies
1
Views
3K
  • Calculus
Replies
9
Views
1K
Replies
3
Views
1K
  • Quantum Interpretations and Foundations
Replies
1
Views
857
  • Classical Physics
Replies
12
Views
7K
  • Special and General Relativity
Replies
3
Views
1K
Back
Top