A Hermitian operator is a type of linear operator in quantum mechanics that is equal to its own adjoint, meaning it satisfies the condition \( A = A^\dagger \). These operators are crucial because they have real eigenvalues and orthogonal eigenvectors, making them essential for representing observable physical quantities. The properties of Hermitian operators ensure that measurements yield real results and that states can be expressed in a coherent manner, especially when dealing with coherent states in systems like the quantum harmonic oscillator.
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