Translation in Spherical Coordinates

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SUMMARY

The discussion focuses on converting wavefunction representations from one spherical coordinate system (r', theta', phi') to another (r, theta, phi) when the origin is shifted. The user seeks to understand how to apply the formula for the shift of origin in spherical coordinates, particularly when dealing with functions that include square roots. The key takeaway is that while the transformation is straightforward in Cartesian coordinates, the presence of square roots complicates the conversion process in spherical coordinates. The user is advised that the azimuthal angle phi remains unchanged during this transformation.

PREREQUISITES
  • Spherical coordinate systems
  • Wavefunction representation in quantum mechanics
  • Mathematical transformations between coordinate systems
  • Understanding of square root functions in mathematical contexts
NEXT STEPS
  • Study the formula for the shift of origin in spherical coordinates
  • Explore mathematical transformations involving square roots in spherical coordinates
  • Learn about plotting wavefunctions in different coordinate systems
  • Investigate the implications of changing coordinate systems in quantum mechanics
USEFUL FOR

Physicists, mathematicians, and students working with wavefunctions in quantum mechanics, particularly those interested in coordinate transformations and spherical coordinates.

karanmohan
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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!
 
Mathematics news on Phys.org
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).
 

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