 ### Update 5_wigner.md

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 ... ... @@ -26,6 +26,13 @@ import plotly.graph_objs as go ` # 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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