Commit dd4cdd49 authored by T. van der Sar's avatar T. van der Sar
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Update 5_wigner.md

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# Lecture 5: The Wigner Quasi-Probability Distribution
!!! success "Expected prior knowledge"
Before the start of this lecture, you should be able to:
- analyze the properties of the coherent state wavefunction
- recall that $\rho(x) = \Psi(x)^*\Psi(x)$ describes a probability distribution
!!! summary "Learning goals"
......@@ -64,7 +71,7 @@ $$
$$
So it's close, but there are two problems with calling $W(x,p)$ a probability distribution:
- In QM, we can only measure one thing at a time, and after measuring our wave function, it collapses, so $W(x,p)$ *cannot* be the probability of measuring both $x$ and $p$, which are non-commuting observables
- In quantum mechanics, we can only measure one thing at a time, and after measuring our wave function, it collapses, so $W(x,p)$ *cannot* be the probability of measuring both $x$ and $p$, which are non-commuting observables
- for some interesting quantum states, $W(x,p)$ can be negative, and since probabilities cannot be negative, we must call it a quasiprobability distribution instead
Note that although $W(x,p)$ can be negative, it must be constructed such that its integrals over $x$ and $p$ are positive, since these do indeed represent probability distributions, as shown above.
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