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sm09
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what is it?
A Hermitian operator is an operator in quantum mechanics that has the property of being self-adjoint, meaning that the operator is equal to its own adjoint. This means that the operator is symmetric with respect to a certain inner product.
Hermitian operators play a critical role in quantum mechanics because they represent physical observables, such as energy, momentum, and angular momentum. These operators have real eigenvalues, making them essential for making predictions about the behavior of quantum systems.
A Hermitian operator acts on a quantum state to produce a new quantum state. The eigenvalues of the operator correspond to the possible outcomes of a measurement of that observable on the quantum state.
Yes, non-Hermitian operators can be used in quantum mechanics, but they do not represent physical observables. Instead, they are used to describe non-unitary processes, such as decay, in quantum systems.
The Hermitian property of an operator ensures that its eigenvalues are real. This is important because the eigenvalues of a Hermitian operator correspond to the outcomes of a measurement, and real eigenvalues represent physically meaningful results.