Odd/even symmetric/antisymmetric

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SUMMARY

Odd/even wavefunctions and symmetric/antisymmetric wavefunctions are distinct concepts in quantum mechanics. Odd/even wavefunctions refer to the spatial symmetry of a single particle's wavefunction, defined mathematically as ##\psi(x) = \pm \psi(-x)##. In contrast, symmetric and antisymmetric wavefunctions apply to systems of identical particles, characterized by the exchange symmetry of the particles, expressed as ##\psi(x_1, x_2) = \pm \psi(x_2, x_1)##. These definitions clarify that while both concepts involve symmetry, they pertain to different contexts within quantum mechanics.

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dyn
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Hi
Are odd/even wavefunctions the same as symmetric/antisymmetric wavefunctions ?
I have seen symmetric/antisymmetric applied to 2 identical particles but is this the same as the odd/even wavefunctions for example applied to a single particle in an infinite well ?
Thanks
 
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In the context that they are usually used, no.
Odd / even typically refer to the spatial symmetry of the wavefunction, whereas the notion of symmetric and antisymmetric states applied to identical particle systems refer to the exchange symmetry of the particles.

Odd / Even: ##\psi(x) = \pm \psi(-x)##
Symmetric / Antisymmetric: ##\psi(x_1, x_2) = \pm \psi(x_2, x_1)##
 
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