# Tag Info

17

This is a good question, and the answer is rather subtle, and I think a physicist and a mathematician would answer it differently. Mathematically, a Hilbert space is just any complete inner product space (where the word "complete" takes a little bit of work to define rigorously, so I won't bother). But when a physicist talks about "the Hilbert space of a ...

17

A quantum state includes the information about a particle's position. Two particles with the same quantum numbers at different locations are in different states, so are allowed by the exclusion principle.

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The signs are important for fixing an out of order machine. Define the states $|\pm\rangle$ as: $$|\pm\rangle = \frac{1}{\sqrt{2}}\left[\left |\text{Working}\right\rangle\pm \left |\text{Down}\right\rangle\right]$$ And we define the observable $O$ as: $$O = |+\rangle\langle + |\ - \ |-\rangle\, \langle -|$$ Suppose then that coffee machine is out of ...

10

Superposition is often claimed, particularly in popular physics texts, to be "an object that is in two states at once", but this is in fact quite misleading. Superposition states, in fact, go beyond this property. Say I have a box, and I claim that it contains a cat that's both dead and alive, with the proviso that when you actually look at it you will ...

9


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