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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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Antisymmetry and coordinate invariance

How can we prove that $\phi(y_1,y_2) = -\phi(y_2,y_1)$? You cannot. Consider $$f_1(y_1,y_2) = \frac{1}{2}(y_1 + y_2),\qquad f_2(y_1,y_2) = \frac{1}{2}(y_1 - y_2).$$ Then, let us take $x_2=0$. In gen …
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