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Kyle.Nemeth
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How do I know if some given state is and eigenstate of some given operator?
Yes, although it may be easier to assume that it is and then derive the result that the eigenvalue is zero.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)?
An eigenstate is a state in which a physical system is in a definite, predictable state. It is characterized by a specific set of quantum numbers and is often represented by a wavefunction.
An operator is a mathematical operation that is applied to a function or a state. In quantum mechanics, operators represent physical observables such as position, momentum, and energy.
To determine if a given state is an eigenstate of a given operator, you need to apply the operator to the state and see if the result is a multiple of the original state. If it is, then the state is an eigenstate of that operator.
When a state is an eigenstate of an operator, it means that the state has a definite value for the corresponding physical observable represented by that operator. This value is called the eigenvalue.
Yes, a state can be an eigenstate of multiple operators. This means that the state has definite values for the corresponding physical observables represented by each of those operators. However, the eigenvalues for each operator may be different.