Where we have interchanged two coordinates ( r j , r k ) of the state function. The usual wave function is obtained using the Slater determinant and the identical particles theory. Using this basis, it is possible to solve any many-particle problem that can be clearly and accurately described by a single wave function single system-wide diagonalizable state. From this perspective, first quantization is not a truly multi-particle theory but the notion of "system" need not consist of a single particle either.