What Are the Dimensions of One-Dimensional Wave Functions?

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seto6
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dimensions of the one-dimensional wave function?

is it [si]=L-1/2?
 
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what would it be for 2-D and 3-D ?
 
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!