# Tag Info

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There is a consistent definition, but it involves a couple of arbitrary thresholds, so I doubt you'd consider it rigorous. The construction $X \gg Y$ means that the ratio $\frac{Y}{X}$ is small enough that subleading terms in the series expansion for $f\bigl(\frac{Y}{X}\bigr) - f(0)$ can be neglected, where $f$ is some relevant function involved in the ...

6

Hertz should be understood to mean "periodic events per second". I your case the events are the display of frames, so yes, you would be perfectly justified in using $\mathrm{Hz}$. That said, as several commenters have already mentioned, the unit "Hertz" does not specify what kind of periodic behavior is being counted. So the author(s) or speaker must make ...

5

I think the answer is no. It generally precedes some approximation method with a bounded error, but there are so many approximations methods in physics -- some rigorous, some nonrigorous -- that it's way too presumptuous to give it a rigorous definition. Generally, it means one of several things: If $a\ll b$, expanding in powers of $\frac{a}{b}$ is ...

4

It is a symbol and an idea used in mathematics too. But the important part is just that $B$ is 'ignorable' relative to $A$. This depends on the level of precision that is being used experimentally. If you're working to a precision of 1 part in 100, then $B$ should not effect the answer to that level of precision. If you're working to 1 part in a million, ...

2

The Hilbert space formulation, sometimes with the explanatory add-on: "where observables are represented by linear operators acting on Hilbert space". Both the wave and matrix sub-formulations are basically shadow-double formalisms for the very same structure.

2

Quantisation does not imply discreteness. If a system has been quantised, we just mean we have taken the set of states, and replaced it by a vector space of states. In other words, one can add states in quantum mechanics, allowing a system to be in two states "at once". Observable quantities become certain operators acting on this vector space of states. As ...

2

I am a professor of theoretical physics (although with a doctorate in applied mathematics), and I had never heard of "approximative reduction" until just now. Following the links in the question, I could get a vague idea of what it meant, but it is not something that I have ever studied or discussed with other scientists. I would conclude that this topic ...

1

For linear operators, the support usually denotes the space which is orthogonal to the kernel (equivalently, the space spanned by the columns of the matrix). Density operators are linear operators, and thus it is used in this sense in the papers you cite. See also this question at math.se or this book from a google search "support of a linear map"

1

I'm not sure what might be confusing you. Assume, as in most cases with the Golden rule, that the transition rate is constant, $\Gamma$. So, for small times, the cumulative transition probability is $W=\Gamma t$. Think of the transition as leakage from a vessel. At $t=0$, no water has been lost, but with a constant rate of leakage, $\Gamma$, the longer ...

1

He is saying that for both the coupled harmonic oscillators and the electron in the chain of atoms: if you start an irregularity in one place, the irregularity will propagate as a wave along the line That's basically just what it means to be coupled. If one starts doing something weird its neighbor will be affected so it will start doing something ...

1

If the first measurement yields the value $A_1$ with certainty, this means the initial state has collapsed into $u_1$ after the first observation. In particular one has, inverting the above back: $$|u_1\rangle =\frac{\sqrt{3}}{2}|v_1\rangle + \frac{1}{2}|v_2\rangle.$$ Now a measurement of the observable $B$ must be performed and then one more measurement ...

1

Apparently Heisenberg referenced the perturbative approach to the quartic oscillator because his advisor and mentor, Max Born, was trying hard to use it in an attempt to push quantum theory past the Bohr model. Born actually invited Heisenberg to work on this problem in his group, and this is where Heisenberg had his breakthrough insight on the need for an ...

1

There are classical and quantum descriptions of the world. One of the differences of quantum description is paying attention to the process of measurement and how it affects the measured system. Description of measurements is an integral part of quantum description. Splitting this is into "realms" doesn't make much sense.

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I don't think that my terminology is suitable, because the term hidden realm carries the connotation of hidden variable theories, which is something else. I don't see them as very different. A hidden variable theory could take as the hidden variable the spinor or the wavefunction as a hidden variable. Many do. Events in the measurable realm ...

1

I think there is a rigorous definition of "$\ll$" sign which is opposite to what you are asking but equally useful notion. You should read this "$\ll$" as is negligible compared to. For example, $f(x) \ll g(x)$ near $x=x_0$ (in a more general context) iff $\frac{f(x)}{g(x)}\to 0$ as $x\to x_0$.

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