The discussion centers on the behavior of two identical particles in a unidimensional box, specifically regarding the implications of their total spin states on the overall wave function. It is established that the total wave function must be antisymmetric under particle exchange, necessitating a symmetric spatial wave function for a singlet spin state and an antisymmetric one for a triplet spin state. The participants emphasize the importance of considering both position and spin when determining the wave function, particularly in non-interacting scenarios.
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It matters. The total wave function, which includes both position and spin, must be antisymmetric under exchange of particles. Thus, the position must be symmetric if the spin is in the singlet state and antisymmetric if the spin is in the triplet state.JamesHG said:I have an "unidimensional" box with two identical particles in. My question is , Does it matter in which total spin state is my total function? I mean , if it is a singlet or triplet , one is antisymmetrical and the other is symmetrical, but I only integrate the function in the spatial coordinates, so any answer?