$$|\psi(x_1,x_2)|^2=|\psi(x_2,x_1)|^2$$(adsbygoogle = window.adsbygoogle || []).push({});

$$\psi(x_1,x_2)=+/-\psi(x_2,x_1)$$

How do they convert they former into the latter one? Is it due to the modulus?

I know the latter can also be written as $$\psi(x_1,x_2)=e^{i\alpha}\psi(x_2,x_1)$$ where the exponential is the phase used to replace +/-.

$$\psi(x_1,x_2)=A[\psi_a(x_1)\psi_b(x_2)\pm\psi_a(x_2)\psi_b(x_1)]$$

As for this, isn't $$\Psi(x_1,x_2)=\Psi_a(x_1) \Psi_b(x_2)$$? Why do we need to add the additional one?

Is it because, the particles are indistinguishable and thus we can add $$\psi_a(x_2)\psi_b(x_1)$$?

If that is the case, won't $$(A\psi_a(x_1)\psi_b(x_2))^2$$ or $$(A\psi_a(x_2)\psi_b(x_1))^2$$ be 0.5(probability) each?

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# I Two Identical non-entangled Particle System

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