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Quantum Sensing and Measurement
Quantum Sensing and Measurement
Commits
8e038356
Commit
8e038356
authored
Nov 18, 2020
by
Gary Steele
Browse files
fixed minus sign
parent
dd4cdd49
Pipeline
#46918
passed with stages
in 6 minutes and 27 seconds
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src/5_wigner.md
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8e038356
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@@ -4,8 +4,8 @@ jupyter:
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@@ -55,7 +55,7 @@ $$
where $p$ is just the 1D scalar momentum, not the momentum operator. We can also form $W(x,p)$ with $
\p
hi(p)$, the Fourier transform of $
\p
si(x)$:
$$
W(x,p) =
\f
rac{1}{
\p
i
\h
bar}
\i
nt_{-
\i
nfty}^{+
\i
nfty}
\p
hi^
*
(p+q)
\p
hi(p-q) e^{2iqx/
\h
bar} dq
W(x,p) =
\f
rac{1}{
\p
i
\h
bar}
\i
nt_{-
\i
nfty}^{+
\i
nfty}
\p
hi^
*
(p+q)
\p
hi(p-q) e^{
-
2iqx/
\h
bar} dq
$$
How should we interpret the Wigner function? It must be something like a probability distribution, as the name suggests. If we integrate $W(x,p)$ over all $p$, we get $|
\p
si(x)|^2$:
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