Eigenvalues give possible measurement results from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
The notion of eigenvalues plays a crucial role in quantum mechanics, providing us with a key insight into the possible outcomes of measurements. When a physical quantity is measured in a quantum system, the result obtained is one of the eigenvalues of the corresponding operator. These eigenvalues represent the observable quantities that can be obtained through measurement, such as energy levels, angular momentum, or position. Eigenvalues are distinct from classical mechanics in that they are not predetermined but rather probabilistic in nature. The act of measurement in quantum mechanics involves a certain degree of uncertainty, with the eigenvalues serving as potential outcomes rather than definite predictions. This inherent randomness is a fundamental aspect of quantum theory, reflecting the probabilistic nature of the underlying physical processes. The eigenvalues of an operator form a discrete...
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