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Quantum Mechanics: Probabilities
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Quantum mechanics describes the instantaneous state of a system with a wave function that encodes the probability distribution of all measurable properties, or observables. Possible observables for a system include energy, position, momentum, and angular momentum. Quantum mechanics does not assign definite values to the observables, instead making predictions about their probability distributions. The wavelike properties of matter are explained by the interference of wave functions.
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Quantum mechanics has provoked a strong philosophical debate. The fundamental problem is that causality and determinism is lost: while the probability distributions evolve according to a well established deterministic law, the values of the observables themselves do not. Because of this, Albert Einstein held that quantum mechanics must be incomplete.
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These are the essential ideas of quantum mechanics. If you find something in this article too preposterous to believe, you're in good company. At first even Einstein refused to believe that probabilities (percent chances) underlie quantum mechanics. Crazy ideas such as this one take awhile for anyone to digest. But keep in mind Faraday's words: "Nothing is too wonderful to be true."
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Since its inception, the many counter-intuitive results of quantum mechanics have provoked strong philosophical debate and many interpretations. Even fundamental issues such as Max Born's basic rules concerning probability amplitudes and probability distributions took decades to be appreciated.
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[N]ow you're ready to solve some interesting quantum mechanics problems. We could give you a situation, ie a particle with a known set of forces acting on it, tell you that we had measured some quantity and gotten a particular result, and then ask you for the probability distribution if you subsequently measure any other quantity. Many problems in quantum mechanics are exactly of this type.
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The main problem with modern physics is that quantum mechanics gives only the probability of an experimental result. Neither the decay of an atomic nucleus nor the fact that it decays at one moment and not another can be properly pictured within the theory. It can only enable you to predict statistically the results of various experiments.
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