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A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.

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Identical particles: why a symmetric or antisymmetric wave function?

$$ \left| \phi(x,y) \right| = \left| \phi(y,x) \right| \implies \phi(y,x) = e^{i \alpha} \phi(x,y) $$ Making exchange twice, we get $$\phi(x,y) = e^{2 i \alpha} \phi(x,y)$$ Hence, $$e^{2 i \alpha} = …
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