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Yes - you have to assume the density of the disk is given as "mass per unit area" - or you can assume a thickness $t$ which will carry forward through all your calculations. The best way to approach problems like this is as a superposition of two objects: one with "positive" mass - the complete disk - and another with "negative" mass: the hole. You can use ...


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It depends on how the quantity in question transforms. Almost always, densities in the form of "stuff per unit volume" and generally the "stuff" (like a charge) is a scalar (a number of things - number of elementary charges), but the volume it is contained in is observer dependent, owing to the Lorentz contraction. Therefore the density is ...


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The one-particle density can be viewed as the localization probability of a particle in the system, with integration over all the state vectors except that of the single particle of interest. For example, suppose you are interested in the positions $\mathbf{x}_i$ of $N$ electrons in a many-electron system in which the $i$-th electron is in spin state ...


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It's true. Special equipment and a long time is required to mix helium and nitrogen. According to one study, a mixture of 2.7% He, 93.3% N at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://pubs.acs.org/doi/abs/10.1021/je60005a002. The helium repeatedly ...



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