Translation in Spherical Coordinates

In summary, the conversation revolves around plotting and manipulating wavefunctions in spherical coordinates. The speaker is seeking help on how to convert a function with a shifted origin in cartesian coordinates to spherical coordinates. The suggested solution is to use the formula for shift of origin in spherical coordinates, which should not be too difficult since the origin is located on the X axis in this case.
  • #1
karanmohan
9
0
Hello, this one is doing my head in. I'm trying to plot and play with wavefunctions by moving the originm, but i need to do it in spherical coordinates.

Suppose i have a function G(r',theta',phi'), centered at the origin of the system r',theta',phi'. I also have a similar G(r'',theta'',phi''). I need to plot these on the same spherical coordinate system (r,theta,phi). The origin of (r',theta',phi') is located at x=x0 of (r,theta,phi). How do i convert G(r',theta',phi') to G(r,theta,phi)?

This problem is easy in cartesian, i just change x to x-x0. However, the functions I'm dealing with have square roots and therefore a simple conversion is not possible.

Thanks in advance for the help!
 
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  • #2
Use the formula for shift of origin in spherical coordinates. ( It won't be very difficult as you have x0 on the X axis - phi wouldn't change).
 

Related to Translation in Spherical Coordinates

What are spherical coordinates?

Spherical coordinates are a system of coordinates used to locate points in three-dimensional space. They consist of a radial distance, an azimuth angle, and a polar angle.

Why is translation in spherical coordinates important?

Translation in spherical coordinates allows us to describe the movement of objects in three-dimensional space using a coordinate system that is more suitable for certain types of problems, such as those involving spherical objects or objects moving in a circular path.

How is translation performed in spherical coordinates?

Translation in spherical coordinates is performed by moving a point in a given direction and distance, while keeping the radial distance and angles constant. This movement is typically represented by a vector in spherical coordinates.

What are the advantages of using spherical coordinates for translation?

One advantage of using spherical coordinates for translation is that it allows for a more intuitive understanding of the movement of objects in three-dimensional space. It also simplifies calculations for certain types of problems, such as those involving rotational motion or objects moving in a circular path.

Are there any limitations to using spherical coordinates for translation?

While spherical coordinates are useful for certain types of problems, they may not be the most efficient or accurate system for other types of problems. Additionally, they can be more difficult to visualize and work with compared to other coordinate systems, such as Cartesian coordinates.

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