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The low-frequency ($\omega\rightarrow 0$), long-wavelength ($q\rightarrow 0$) conductivity of an electron gas in the random phase approximation depends on the order in which those two limits are taken. Intuitively, if you take the $\omega\rightarrow 0$ limit first, you're talking about a static, long-wavelength potential to which the electrons adjust, so ...


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It seems to me that it's not 'vectors' or 'vector algebra' which these students aren't grasping. Its the connection between a given 'physical phenomenon' and a corresponding 'mathematical representation'. I suspect this has something to do with conceptualising the physics rather than the mathematics. To put is simply: Physics $\neq$ Mathematics When ...


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Starting from scratch I would propose an order of topics to study as follows: Kinematics (motion) Dynamics (forces) Rotational kinematics and dynamics Collisions (momentum and impulse) Vibrations and waves Thermodynamics Electricity (DC) Electricity (AC) Magnetic fields and forces Electromagnetic waves Light (optics, photons) Quantum mechanics ...


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I can't comment on the up-till-now, but here's something to try for the "now-and-henceforth". I suspect that many student difficulties have in the past been left unhelped by the fact that lecture courses were "linear" (no pun meant here): there was a set coursework and a set way of thinking about concepts that the lecturer or teacher chose that students ...


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An Illustrated Guide to Relativity - Tatsu Takeuchi A very enjoyable book on special relativity for beginners. It covers the basics (Lorentz transforms, length contraction, time dilation, velocity addition, twin paradox,...) using spacetime diagrams rather than equations. It's a fun and intuitive introduction. To give you an idea: this is an illustration ...


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For example, in statistical mechanics, you get different results for systems with spontaneous symmetry breaking, say, for a ferromagnetic, depending on whether you first take the limit $N\rightarrow\infty$ or $H\rightarrow 0$ when calculating average magnetization (http://www.encyclopediaofmath.org/index.php/Quasi-averages,_method_of ).


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Good question. When we build a theory we start from a couple of assumptions that we BELIEVE that are valid, i.e. in the everyday life, and/or in previous experiments, they were confirmed. From this point we use mathematics and obtain other results. As long as we need our new results for proving even more theorems, things may be fine. But a physical theory is ...


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Newton described his theories with maths, and they worked great, until Einstein came along and found that as objects approached the speed of light, Newwton's maths broke down. Empirical evidences trumps theory.


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Just two cents: I assume you already introduced Newton's laws, you can say that is something like "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force" yu can explain that from the other two Newtons laws it can be shown that the first law naturally ...


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I suggest a way: bring a toy of a gyroscope form, put it on a table, and give it a brief torque. Although you don't act anymore on the toy, it continues to rotate. Ask your students WHY does it happen. I assume that they learned about the conservation of LINEAR momentum. So, we have an analogy: a body in linear movement keeps moving as long as no force ...


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The most obvious application of Fermi's Golden Rule is the transition probablity from 2p to the 1s state in the hydrogen atom. The rate of transition is given by product of the two wave functions with the Hamiltonian, which we can take to be an oscillating potential in the z direction: $$\langle 2 \, p |\, z \sin \omega t \, | 1 \, s\rangle $$ This is the ...


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The original use of the algorithm known as the Fermi rule is Dirac's calculation of Einstein's absorption coefficient of an ensemble of atoms: P.A.M. Dirac, On the theory of quantum mechanics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (1926), 112, p. 661-677 http://dx.doi.org/10.1098/rspa.1926.0133 ...


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I have helped some school students through a course which was taught with Matter and Interactions which focussed on using physics principles to program computer simulations. Because of the programming, my students were comfortable with vectors from the first week. The computer made the vectors visual and as simple to manipulate as variables containing ...



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