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Inquisiter
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Ok, so when the Sch. eq. is solved for hydrogen (H-like atom), we get various eingenstates of energy and angular momentum. For n=2, l=1, we get m=1, m=0, m=-1. The 1,0,-1 represent the z component of l. We also talk of hydrogen as having (for n=2, l=1) three p orbitals. Am I correct that these three orbitals are not the eingenstates of the z component of l? From what I understand (and I don't understand this well), one of them is the eigenstate of the z comp. of l with eigenvalue 0 (the one which is parallel to the z axis), each one of the other two orbitals, however, are actually superpositions of m=1 and m=-1 eigenstates. So, for example, the y component of the angular momentum is 0 for the orbital which is parallel to the y axis, while the y component for the eigenstate of the z comp. of ang. mom. with m=1 is not defined. So I take it that the p orbital parallel to the y-axis is a superposition of TWO eingenstates (with eigenvalues 1 and -1) of the z comp. of l. Can we have superpositions of the three eigenstates of the z comp. of l which produce p orbitals which are not perpendicular to each other. Why are the orbitals perpendicular in an H atom? Is it simply because it minimizes electron-electron repulsion? Also, I'm confused by the Pauli exclusion principle. It says that no two fermions can be in the same quantum state. But if we have three eigenstates (as we do for n=2, l=1), can't we produce an infinite number of states (each one with the same energy) by superimposing the three eigenstates(each time with different coefficients)? So when we talk about quantum states as they relate to the Pauli principle, must these states be linearly independent or what?? I know that we can place only 6 electrons in n=2, l=1 state, not an infinite number of electrons.
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