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The fractional dimensional space approach (FDSA) can be adopted to introduce flexibility in examining optoelectronic properties in anisotropic systems (quantum dot, wells etc). Here the material are fitted to models that utilize a variable dimension, (alpha) which has provided good agreement with experimental results in many works. This is because the ...


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In the long run I don't think it matters much which of the two you study now. If you truly understand calculus in 2-3 dimensions, you won't have too much trouble generalizing your understanding to $N$ dimensions. On the other hand, if you want to do research in condensed matter, you will need linear algebra anyway, so there's no harm in picking up that topic ...


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This is directly associated with limit.


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The area element of the surface of a sphere is $\sin(\theta) r^2 d\theta d\varphi$. You can verify this yourself: $$\int_0^{2\pi}\int_0^\pi \sin(\theta)r^2 d\theta d\varphi=(2\pi)(-\cos(\pi)-(-\cos(0)))=4\pi r^2$$. So, if you integrate over only the $\varphi$ direction, you get the area of an infinitesimal loop: ...


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Calculus works in two senses and fails in a third one: as a mathematical theory, it is well-founded, independently of Newton and Leibniz invention. For operations with space and velocity, it also works, because these quantities are not even discrete in usual quantum mechanics, and the only argument can come if you go "atomistic"; then it must be substituted ...


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Even though calculus was invented in order to study a physics problem, it is a mathematical tool that is very general, that also describes discrete situations. But if I am not mistaken a fundamental principle of the quantum world is that things can only take on disjointed, discrete values You are confusing necessary and sufficient. It is sufficient to ...


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It is true that accelerating charges radiate energy in the form of electromagnetic radiation. However, the relationship is not a naive ratio between the acceleration and the amplitude of the electromagnetic wave. Rather, you need to invoke Maxwell's equations. Specifically, there is Ampere's law: $$\nabla\times{\bf B}={\bf J}+\frac{\partial{\bf ...



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