Is the position of an electron part of his quantum state? Pauli exclusion principle I have a problem regarding the Pauli exclusion principle which as far as I understand states that two or more identical fermions cannot occupy the same quantum state. 
So is the position ($r_1$) of an electron in an atom part of its quantum state ?


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*If yes, why do two electrons in  a $ 1s$ orbital have opposite spins despite having different positions? 


I am guessing that its related to Heisenberg uncertainty principle as follows: since the electrons' position's  aren't known with complete precision, they may coincide.
 A: Electrons don't have a single well-defined position. They have a position wavefunction, which is related to a probability distribution that an electron will be at a particular position. The Pauli exclusion principle says that two fermions cannot have the same state. The state includes the particle identity, the spin, and, among (possibly) other things, the wavefunction. Two electrons with the same spin and the same wavefunction are in the same state, so this is forbidden by the Pauli exclusion principle.
For electrons in an atom, or subject to some other time-independent potential, electrons in their lowest-energy state occupy one of a discrete set of possible wavefunctions. Since they are discrete, we can number them; these quantum numbers are a shorthand for referencing a particular state compatible with a particular potential. This means that the Pauli exclusion principle can also be restated as: two identical fermions cannot have the same set of quantum numbers.
A: If you look at the periodic table, which has ordered the elements according to their behaviour, you can see that there are 2, 2+8 and 2+8+8 electrons in the first three periods. The amazing thing is that you can imagine (please only for yourself) the electrons as bar magnets. In helium they are standing head to foot opposite each other and in 8 electrons they are arranged in the edges of a cube, 4 with the north pole to the nucleus and 4 with the south pole.
This image is helpful for me for understanding the founded empirically Pauli principle or for example the symmetrical behavior of methan CH4.
