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I'm not sure a 2d structure will give you the required phase information unless you can compute that before printing, in which case you are making a hologram. What about some 3d structure that is on the same scale? I don't know what the finest incandescent bulb filament is you can acquire, but perhaps something like that might work. Also, traditional ...


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Reflection diffraction gratings can be made very easily from compact discs (CDs). You get a diffraction pattern simply by reflecting a laser pointer from a CD. If you know the wavelength of the pointer you could work out the groove spacing. Someone has kindly provided a lab script for that very experiment. Or see this one. If you want to do more than ...


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With one change this should work. For a transmission experiment you'd probably be better printing on a transparency. I haven't tried this, mind you, but laser printers can achieve the necessary scale quite easily. You might be able to get it to work in reflection mode printed to paper, but you are going to lose a lot of intensity. Didn't work with the ...


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Classically, the gravitational force experienced by a mass $m$ above the Earth is given by the familiar, $$F=G\frac{Mm}{r^2}$$ where $M$ is the mass of the Earth. In other words, a mass will experience a force which continually decreases as it distances itself away from the Earth. Now suppose the Earth was a flat infinitely$^{\dagger}$ large plane in ...


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(1) We shall never have the right to affirm categorically of any one of the principles of the mechanical and physical theory, that it is true. (2) We are not allowed to affirm of any one of the principles on which the mechanical and physical theory rests, that it is false, so long as there has been no discovery of phenomena that disagree with the ...


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Because you dont need general relativistic (tensors ,differential geometry etc) calculation to send a rocket to the moon.


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Classical mechanics are very important for everyday physics. For the energy scales, relative velocity differences, and mass scales that we experience is our everyday lives, Newtonian physics provide us with an extremely valuable tool of predicting outcomes of events. In other words Newtonian physics are an accurate enough approximation to the more precise ...


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Two reasons. First, I strongly recommend Asimov's essay Relativity of Wrong that explains very concisely and clearly why questions such as this one are more wrong than Newtonian physics. Second, the concepts of Newtonian physics are necessary for explaining pretty much anything in physics, including general relativity and quantum mechanics. These ...


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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 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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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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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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When vectors are introduced, it should be empathized that a vector has 2 components, a magnitude and a direction. You can make a list of non-vectors and vectors (mass, speed velocity, acceleration, etc) which you can put on a quiz. Also, any equation that utilizes vectors is incorrect if the vector symbol is not included.


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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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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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Linear operators are equivalent to rotation matrices, so they do not neccessarily commute (if n>2). Thus, in general, you cannot exchange the order of the limits. However, as Pedro Shor commented: "physicists are clever enough not to present calculations that don't work". What this means is that physicists still can assume that the operators commute, and ...


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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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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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Well, could you start just with perturbation theory, time dependent, and transition amplitudes? Simple interaction and transition between states. If they are familiar with time evolution operator and Dirac bra-ket notation of course. In solid state physics as far as I know, you can use it to calculate scattering of electrons off phonons, so again, its ...


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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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This is no different than the linear motion case. The generator moves because torque is applied to it. In response it applies torque to the shaft turning it. The net torque on the system is zero but individual components feel (opposite) net torques. This is absolutely fundamental to understanding any Newtonian mechanics.


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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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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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