What Are the Dimensions of One-Dimensional Wave Functions?

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Discussion Overview

The discussion centers on the dimensions of one-dimensional wave functions and extends to the dimensions of wave functions in two and three dimensions. It involves mathematical reasoning related to the units of wave functions in different spatial dimensions.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant asks about the dimensions of the one-dimensional wave function, suggesting it may be [si]=L-1/2.
  • Another participant agrees with this dimension for the one-dimensional case.
  • A subsequent participant inquires about the dimensions for two-dimensional and three-dimensional wave functions.
  • One participant proposes that the units for n-dimensional wave functions should be L-n/2 to ensure that integrating its square over an n-dimensional volume yields a unitless area.
  • This leads to the conclusion that for two dimensions, the dimension would be L-1, and for three dimensions, it would be L-3/2.

Areas of Agreement / Disagreement

Participants generally agree on the proposed dimensions for one, two, and three-dimensional wave functions, but the discussion remains open to further exploration of these concepts.

Contextual Notes

Assumptions regarding the integration process and the definitions of wave functions are not fully detailed, and the discussion does not resolve potential nuances in dimensional analysis.

Who May Find This Useful

Readers interested in quantum mechanics, wave functions, and dimensional analysis in physics may find this discussion relevant.

seto6
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dimensions of the one-dimensional wave function?

is it [si]=L-1/2?
 
Physics news on Phys.org
yes.
 
thanks man!
 
what would it be for 2-D and 3-D ?
 
When you integrate its square over an n-dimensional volume, you want to get a unitless area, so its units have to be L-n/2.
 
so for 2D it would be L-2/2 = L-1..for 3D it would me L-3/2

just making sure...

thanks for you replies!
 

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