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Quantum Processes Systems, and Information by Michael Westmoreland, Benjamin Schumacher

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10  A particle in space

10.1  Continuous degrees of freedom

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The quantum systems we have discussed so far have been described by finite-dimensional Hilbert spaces. Basic measurements on such systems have a finite number of possible outcomes, and a quantum state predicts a discrete probability distribution over these. Now we wish to extend our theory to handle systems with one or more continuous degrees of freedom, such as the position of a particle that can move in one dimension. This will require an extension of our theory to Hilbert spaces of infinite dimension, and to systems with continuous observables.

There is a philosophical issue here. ...

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