Hermitian Operator: Definition & Overview

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A Hermitian operator is defined as an operator in quantum mechanics where the diagonal elements of its matrix representation are real, and the off-diagonal elements are complex conjugates of each other. This property ensures that the Hermitian conjugate of the operator equals itself, making it crucial for representing measurable quantities in quantum mechanics. The eigenvalues of Hermitian operators are always real numbers, which corresponds to the outcomes of measurements. For instance, measuring the z-directed spin of an electron in a specific state yields a definite result, demonstrating the operator's role in the measurement process. Understanding Hermitian operators is essential for grasping the fundamentals of quantum mechanics.
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an operator that is hermitian!

in a matrix representation, it means that the diagonal Mii is real, and any Mij is the complex conjugate of Mji. this gives the hermitian conjugate of M (transpose and conjugate) is itself.or... google Hermitian

it represents a measurable quantity in QM.

ps.
am i right?
 
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This question is well enough described in a any QM textbook. You do not make much effort to look there. In simple, Hermitian operator is the observable represetation, or if not rigorously speaking, it reflects the measurement procedure in a some quantum state. For example, let we have an spin-up directed electron state \left | + \right>. Measurement of the z-directed spin by \hat S_z in this state is reflected in the equality \hat S_z \left | + \right> = +\hbar/2 \left | + \right>. This mean the result you will get is +\hbar/2. A key feature of a Hermitian operator is real numbers of their eigenvalues.
 
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Thread 'Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'

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