What is the physical meaning of the parity of a wavefunction?

In summary, the parity of a wavefunction is a property that describes how the wavefunction changes under inversion, and can be either even or odd. It is determined by examining the transformation of its coordinates under inversion, and has significance in understanding the symmetry of physical systems. The main difference between even and odd parity is their behavior under inversion, and a wavefunction can only have one parity, although it can be a mixture of even and odd functions.
  • #1
opous
16
0
Can anyone help me understand what is meant by the "parity of a wavefunction"?

I know in terms of even/odd parity, that:

[tex]P \Psi(x,y,z) = \pm \Psi(x,y,z)[/tex]

ie, P = +/- 1

But I don't know what "parity of a wavefunction" physically means...
 
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  • #2
The P operator turns [tex]{\vec r}\rightarrow -{\vec r}[/tex].
 
Last edited:
  • #3
you can also relate this to ordninary functions.

P(cos(x)) = cos(-x) = cos(x) ; so cos is an even function -> Symmetric

P(sin(x)) = sin(-x) = -sin(x) ; so sin is an odd function -> Anti-Symmetric
 

What is the parity of a wavefunction?

The parity of a wavefunction is a property that describes how the wavefunction changes when its coordinates are inverted. It can be either even (+1) or odd (-1).

How is the parity of a wavefunction determined?

The parity of a wavefunction is determined by examining the transformation of its coordinates under inversion. If the wavefunction remains unchanged, it is even, and if it changes sign, it is odd.

What is the physical significance of the parity of a wavefunction?

The parity of a wavefunction is important in understanding the symmetry of physical systems. A system with even parity is symmetric under inversion, while a system with odd parity is asymmetric.

What is the difference between even and odd parity?

The main difference between even and odd parity is their behavior under inversion. Even parity wavefunctions remain unchanged, while odd parity wavefunctions change sign when coordinates are inverted.

Can a wavefunction have both even and odd parity?

No, a wavefunction can only have one parity. However, a wavefunction can be a linear combination of even and odd functions, resulting in a mixed or undefined parity.

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