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Post by Sevyrs on Nov 23, 2017 23:30:41 GMT
Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. these are known as Eigenvalues of the observable and the corresponding wave functions are called Eigenfunctions. The Eigenfunctions are those Eigenfunctions which are definite and single valued. When something is in the condition of being definitely 'pinned down', it is said to possess an Eigenvalue. For example, if the position of an electron has been made definite, it is said to have an Eigenvalue of position. The term Eigen can be roughly translated from German as inherent or as a characteristic. The German word 'Eigen' was first used in this context by the mathematician David Hilbert in 1904.
Energy Eigen values for a free particle:
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