What Does It Mean When an Operator Has Two Normalized Eigenstates?

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Slepton
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I am confused about operators and eigenstates. What does "an operator has two normalized eigenstates" mean ? Is there a way I can make a physical interpretation ? How are measurements made with these ?
 
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Slepton said:
What does "an operator has two normalized eigenstates" mean ? Is there a way I can make a physical interpretation ?
It means that when you make the measurement corresponding to the operator you will measure one of two values.
 

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