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Elementary question about quantum mechanics

Think thet there are two particles 1 and 2.  Should we describe them by a single multivariable wave function Y(1,2)?  Or should we rather describe them separately and respectively by two singlevariable wave functions Y(1) and Y(2)?

Think two extreme cases, the first being the two electrons in a Helium atom, and the seccond the two free electrons each being located at the opposite sides of the universe.  But keep in mind at the same time that in the latter case the electrons might have interaction a long, long time ago in the past.

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