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Physics
Quantum Physics
The postulate of Quantum Mechanics and Eigenvalue equation
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[QUOTE="Nugatory, post: 5456199, member: 382138"] The postulate says that if you measure a given observable, the result will be one of the eigenvalues of that observable. However, the system state is not necessarily an eigenstate before you measure; it may be a superposition of several different eigenstates with different eigenvalues and then your measurement may yield any of several different results. Formally, you prepare an ensemble of systems all in the same initial state and measure the observable on each instance. If the initial state is an eigenstate of the observable, you will get the corresponding eigenvalue on every measurement and ##\sigma## will be zero. However, if the initial state is a superposition you will get different results (all eigenvalues of one of the many eigenstates making up the superposition) on the different measurements and ##\sigma## will be non-zero. For a number of reasons, it is not possible to prepare a system in an exact eigenstate of the position operator, so ##\sigma_x## will always be non-zero. [/QUOTE]
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The postulate of Quantum Mechanics and Eigenvalue equation
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