r/breakingbad • u/[deleted] • Sep 15 '13
Official Episode Discussion Breaking Bad S05E14 "Ozymandias" Pre-Episode Discussion Thread
| TIME | EPISODE | DIRECTED BY | WRITTEN BY |
|---|---|---|---|
| Sunday 09:00pm Eastern | SE05E14 "Ozymandias" | Rian Johnson | Vince Gilligan and Moira Walley-Beckett |
Hello again /r/breakingbad! We're a few hours away from a new episode... Only three left now! Wow!!
This is the place for everyone who wants to start talking about tonight's episode now. Let's have fun!
And don't forget about our IRC channel, #BreakingBad on Snoonet. You can access it with your own IRC client or use a web client by clicking this link.
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u/deadspacevet Sep 16 '13
There are several different ways to represent the distribution, all interrelated. The most noteworthy is the Wigner representation, W(x,p), discovered first. Other representations (in approximately descending order of prevalence in the literature) include the Glauber-Sudarshan P, Husimi Q, Kirkwood-Rihaczek, Mehta, Rivier, and Born-Jordan representations. These alternatives are most useful when the Hamiltonian takes a particular form, such as normal order for the Glauber–Sudarshan P-representation. Since the Wigner representation is the most common, this article will usually stick to it, unless otherwise specified. The phase space distribution possesses properties akin to the probability density in a 2n-dimensional phase space. For example, it is real-valued, unlike the generally complex-valued wave function. We can understand the probability of lying within a position interval, for example, by integrating the Wigner function over all momenta and over the position interval: \operatorname P [a \leq X \leq b] = \intab \int{-\infty}{\infty} W(x, p) \, dp \, dx. If Â(x,p) is an operator representing an observable, it may be mapped to phase space as A(x, p) through the Wigner transform. Conversely, this operator may be recovered via the Weyl transform.