The one-dimensional Schrödinger operator is a mathematical operator used in quantum mechanics, typically represented as $-\frac{d^2}{dx^2} + V(x)$, where $V(x)$ is the potential energy function. This operator describes how quantum particles behave in a one-dimensional space and is crucial for solving the time-independent Schrödinger equation, which provides insights into the energy levels and wave functions of quantum systems.
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