I System of bosons

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In a system of bosons, the overall wave function must be symmetric. While the spatial and spin functions can individually be antisymmetric, symmetry can still be achieved when considering the entire wave function. For systems with more than two particles, the complexity increases, allowing for mixed symmetry in the components. However, regardless of the individual characteristics of the spatial and spin functions, the net wave function remains symmetric. This fundamental property is crucial for understanding bosonic systems.
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If I have a system of bosons described by a wave function that can be separated into a spatial function and a spin function, do the spatial and spin functions have to be both symetric? Or can they be anti-symetric and symetry be attained only when we consider the whole wave function?
 
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ananonanunes said:
If I have a system of bosons described by a wave function that can be separated into a spatial function and a spin function, do the spatial and spin functions have to be both symetric? Or can they be anti-symetric and symetry be attained only when we consider the whole wave function?
The whole wave function must be symmetric. The components may both be antisymmetric.
 
With more than two particles things become more complicated. The space and spin wave functions can have mixed symmetry, neither symmetric nor asymmetric. The net function must be symmetric, though.
 

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