Spectral Theory
The position operator is a fundamental concept in quantum mechanics, represented by the operator \\hat{x} that acts on the wave functions in a Hilbert space to determine the position of a particle. It plays a crucial role in spectral theory, especially in the context of unbounded self-adjoint operators, where it is used to analyze the spectrum of possible measurement outcomes and understand essential self-adjointness conditions that guarantee the operator's well-defined nature in quantum systems.
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