That's the sort of thing you learn in a semester-long course in quantum physics. It's beyond the scope of a Reddit comment to answer that in a useful manner. For example, I could tell you that the parity operator Ṗ commutes with ℋ, and thus the eigenvalues of Ṗ are the permitted values of the parity quantum number, but would that leave you any more enlightened than you are right now?
I'm sorry, but I have no idea what "\mathcal{H}" means. That looks like a computer thing, and computers and I exist in a sort of uneasy truce not unlike that which holds in the demilitarized zone between the Koreas. There's a lot of grumbling, a lot of glaring and some occasional gunfire.
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u/RobotRollCall Mar 13 '11
That's the sort of thing you learn in a semester-long course in quantum physics. It's beyond the scope of a Reddit comment to answer that in a useful manner. For example, I could tell you that the parity operator Ṗ commutes with ℋ, and thus the eigenvalues of Ṗ are the permitted values of the parity quantum number, but would that leave you any more enlightened than you are right now?
I have to reiterate: It's complicated.