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Can the eigenvalue for a quantum mechanical operator be zero?

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closed as too broad by Tyberius, Mithoron, paracetamol, Pritt Balagopal, ron Aug 24 '17 at 15:04

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ yes it could be, here you could find a satisfying answer link $\endgroup$ – Jaafar Mehrez Aug 24 '17 at 11:31
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    $\begingroup$ The question is way broader than you seem to think; you might want to be more specific. As it stands now, the answer is "yes", but it is a really useless "yes", about the same level as if you were asking "can a difference of two numbers be zero". Sure it can; so what? $\endgroup$ – Ivan Neretin Aug 24 '17 at 11:31
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$S_z$ (spin along the z-axis) is a QM operator, and it frequently is zero - such as in closed-shell molecules.

Also note that the zero energy point of quantum mechanics can be defined in more than one way: some quantum chemistry programs use "all electrons and nuclei at infinite separation", whereas some solid state programs used "neutral atoms at infinite separation". Nevertheless, they evaluate the total energy.

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