Exploring the Dimensions of Wave Functions

In summary, the dimensions of a wave function vary depending on the physical quantity it represents and provide important information about the system. These dimensions must be consistent with the corresponding physical quantity and can change through mathematical operations. However, the dimensions of a wave function do not impact its normalization, which is determined by its square integral.
  • #1
seto6
251
0
dimensions of the one-dimensional wave function?

is it [si]=L-1/2?
 
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  • #2
yes.
 
  • #3
thanks man!
 
  • #4
what would it be for 2-D and 3-D ?
 
  • #5
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.
 
  • #6
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!
 

Related to Exploring the Dimensions of Wave Functions

1. What are the dimensions of a wave function?

The dimensions of a wave function depend on the physical quantity it represents. For example, the dimension of a position wave function is length, while the dimension of a momentum wave function is mass times velocity.

2. What is the significance of the dimensions of a wave function?

The dimensions of a wave function provide information about the physical quantity it represents. This allows us to understand the behavior of the system and make predictions based on the wave function.

3. How are the dimensions of a wave function related to the dimensions of physical quantities?

The dimensions of a wave function must be consistent with the dimensions of the corresponding physical quantity. This means that the units of the wave function must match the units of the physical quantity it represents.

4. Can the dimensions of a wave function change?

Yes, the dimensions of a wave function can change depending on the physical quantity it represents. For example, a position wave function can be transformed into a momentum wave function through mathematical operations.

5. How do the dimensions of a wave function affect its normalization?

The dimensions of a wave function do not affect its normalization. The normalization of a wave function is determined by its square integral, which is independent of its dimensions.

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