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Dixanadu
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Homework Statement
Hey guys, I'll type this thing up in Word.
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A coherent state is a type of quantum state that represents a classical-like state of a quantum system. It is characterized by a well-defined phase and a minimum uncertainty in the position and momentum of the system.
To check if a coherent state is an eigenfunction of an operator, you can apply the operator to the coherent state and see if it returns the same state multiplied by a constant. If it does, then the coherent state is an eigenfunction of that operator.
If a coherent state is an eigenfunction of an operator, it means that the state is a solution to the corresponding eigenvalue equation. This allows us to easily calculate the expectation value of that operator for the coherent state.
Yes, a coherent state can be an eigenfunction of multiple operators. This is because different operators can have the same eigenfunctions and eigenvalues.
The eigenvalue of a coherent state is related to its classical counterpart through the uncertainty principle. The coherent state has a minimum uncertainty, which is equivalent to having a well-defined classical value for the corresponding observable.