Aha. On Sunday afternoons after lunch I relax by reading my favourite science blogs, and I'll be reading Quanta. So I'll enjoy reading that article later today.
Say I have Schrödinger's cat in a sealed box. It is neither alive nor dead.
Given that cats have a lifespan of ~20 years, if I wait a thousand years, I should be able to infer with 100% certainty that the cat is dead. But if I can say with 100% certainty that the cat is dead, then I have "collaps...
Dirac equation reduces dofs of the Dirac spinor by half, while KG equation doesn't. I have two questions: what if we add interaction terms? That changes the EOM. Shouldn't it mess with the number of dofs in general, given that we define on-shell dofs?
And also I didnt quite understand what does 1st order nature of Dirac equation has to deal with its reduction of dofs? I just know that boosting to the rest frame and using explicit form of gamma matrices projects out half components of spinors. But what does this have to do with 1st order nature?
If the following is the pdf of a qho in a coherent state: $$|\Psi(x; t)|^2 = \frac{1}{\sqrt{\pi} x_0} \exp\left\{-\frac{[x - x_0 \sqrt{2} |\lambda| \cos(\omega t - \phi)]^2}{x_0^2}\right\},$$ where $x_0=\sqrt{\frac{\hbar}{m\omega}}$.
When the mass becomes large, the standard deviation on the expression would go to zero
As such the pdf becomes a delta-function x=Acos(\omega t - \delta)
Can anyone explain to me the gaussian with vanishing width?
In wikipedia te explanation I found is quite complicated
@imbAF I don't know what you want to know, but you can use a limit of a sequence of functions, the limit can involve a discrete or continuous parameter: I usually like to use the following family of functions: $$ \delta_n(x) = \sqrt{\frac{n}{\pi}}e^{-nx^2}, n = 1,2,3,...$$ in fact you can easily see that $\int_{\mathbb{R}}\delta_n(x) = 1$.
Now you just have to prove that $\lim_{n \to \infty}\int_{\mathbb{R}} \delta_n(x)F(x) = F(0)$ for a generic smooth test function, which you can assume to be limited
anyways, many rigorous proofs of what you are searching for exist online: for example take a look at this very elegant one
