Separation of Variables Spherical Coordinates

In summary, the learner is struggling with a question from a past exam and has attached their attempt and relevant equations. They mistakenly added instead of subtracting and are now able to solve the problem. The scan is too large to attach so a URL is provided for reference.
  • #1
cooev769
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Homework Statement



So I'm doing a question from one of my past exams as attached, there are no copy right issues with this document that I know of and have asked my lecturer who wrote the exam and he said I am welcome to upload it. The question is 1)b)iv), my attempt is attached. I end up with a 2l+1 where there should just be 1, can anybody tell me where I went wrong?

Homework Equations



Relevant equations are attached in the past exam

The Attempt at a Solution



My scan is too large to attach so please use the url provided. Thanks

http://tinypic.com/r/4ki9w5/8
 

Attachments

  • phsi332_2012_s2.pdf
    512.9 KB · Views: 279
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  • #2
Solved I was adding the two instead of subtracting them. I can do electrodynamics but I can't do simple addition. Time to go and cuff my primary school teacher.
 

1. What is the concept of Separation of Variables in Spherical Coordinates?

The concept of Separation of Variables in Spherical Coordinates refers to the technique used to solve partial differential equations in spherical coordinate systems. It involves breaking down the solution into simpler functions that depend on only one variable each, making the problem easier to solve.

2. What are the three variables used in Spherical Coordinates?

The three variables used in Spherical Coordinates are radius (r), inclination angle (theta), and azimuthal angle (phi). These variables represent the distance from the origin, the angle measured from the positive z-axis, and the angle measured from the positive x-axis, respectively.

3. How is the Laplace Operator expressed in Spherical Coordinates?

The Laplace Operator in Spherical Coordinates is expressed as 1/r^2 * (∂/∂r) * (r^2 * ∂u/∂r) + (1/r^2 * sin(theta)) * (∂/∂theta) * (sin(theta) * ∂u/∂theta) + (1/r^2 * sin^2(theta)) * (∂^2u/∂phi^2), where u represents the function being solved for.

4. What is the significance of the Separable Solutions in Spherical Coordinates?

The Separable Solutions in Spherical Coordinates are significant because they allow for the decomposition of a complex partial differential equation into simpler ordinary differential equations, which can then be solved using standard techniques. This simplifies the problem and makes it easier to find a solution.

5. How is the Separation of Variables technique applied in real-world scenarios?

The Separation of Variables technique is commonly used in engineering and physics to solve problems involving spherical symmetry, such as heat conduction in spherical objects or the behavior of electric fields around spherical charges. It is also used in solving problems in quantum mechanics, such as the behavior of electrons in atoms.

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