When is a given state an eigenstate of a given operator?

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SUMMARY

This discussion focuses on determining whether a given state is an eigenstate of a specific operator within the framework of quantum mechanics, utilizing Dirac notation and matrix representation. The primary method involves starting with the eigenvalue equation and demonstrating that the state does not satisfy the conditions to be an eigenvector of the operator. A suggested approach is to initially assume the state is an eigenstate and derive that the corresponding eigenvalue is zero if it is not. The conversation highlights the theoretical aspects of eigenstates and operators, emphasizing the importance of mathematical representation.

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  • Understanding of quantum mechanics principles, particularly eigenstates and operators
  • Familiarity with Dirac notation for quantum states
  • Knowledge of matrix representation of operators and states
  • Ability to manipulate eigenvalue equations in a mathematical context
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Quantum mechanics students, theoretical physicists, and researchers focusing on the mathematical aspects of quantum states and operators.

Kyle.Nemeth
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How do I know if some given state is and eigenstate of some given operator?
 
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This is an extremely broad question. Are you talking about experiments or theory?
 
I am referring to theory. I may have posted this in the wrong category as well, I'm not sure. But I'm trying to prove that some given state is not an eigenstate of some given operator. I'm doing this all in Dirac notation and matrix representation. So, should I start with the eigenvalue equation and show that the given state is not an eigenvector of the operator (Again, I know the operator and the state in matrix form)?
 
Kyle.Nemeth said:
So, should I start with the eigenvalue equation and show that the given state is not an eigenvector of the operator (Again, I know the operator and the state in matrix form)?
Yes, although it may be easier to assume that it is and then derive the result that the eigenvalue is zero.
 
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Thank you for the help Nugatory, much appreciated.
 

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