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Yes, parity is really violated, even if neutrinos are massive. You seem to be confusing the relationship between parity, helicity, and chirality in the modern standard model with the physical symmetry operation of spatial inversion. Wu's experiment did not measure neutrino helicity. Wu and collaborators prepared a thin layer of a beta-emitting nucleus ...

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The big mystery is: why should nature prefer one direction over another? And the answer is still unknown. From wikipedia: The experiment's purpose was to establish whether or not conservation of parity (P-conservation), which was previously established in the electromagnetic and strong interactions, also applied to weak interactions. If ...

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While the accepted answer is very clear, I'll write an operator proof. The $\hat{p^2}$ in $\hat{H}$ commutes with $\hat{\mathbb{P}}$ (the parity operator). So, to show that $\hat{H}$ and $\hat{\mathbb{P}}$ commute, we have to show this: $[\hat{V},\hat{\mathbb{P}}]=0$ Note that since $V(x)$ is a symmetric function i.e. even function, it is an eigenfunction ...

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The ground state nuclear spin quantum number and parity, $J^{\pi}$ for all even-even nuclei is $0^+$. The isospin can vary, but for the ground state of even-even will probably be either 0 or 1. The isospin quantum number, $I$, is limited to the range of $$\frac{|Z-N|}{2}\le I \le \frac{Z+N}{2}.$$ The $J$ for odd-mass-number nuclei will be a half-integer ...

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The quantum numbers are "parameters" that characterize the states of a particle or an atom. If I understand correctly what is your question, it is not always possible to measure directly all the quantum numbers, but sometimes you have to use some tricks to calculate them (for example special experiments or calculations based on the properties of the quantum ...

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