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The method you are using here is Euler-Cromer. It only really works for sytems with two variables (although I guess it could be modified for systems with any even number of variables - e.g. find $x, y, z$ then $vx, vy, vz$). There is a more accurate method, which is more general, but more complicated to program. This is the 4th order Runge Kutta (RK) ...


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It amuses me how often the cart is set in front of the horse in answers at this site. It is the data that drive theoretical formulations, not theoretical formulations the data. It was from the spectral lines of the hydrogen atom that the Schrodinger equation was established and the whole construct of the theory of quantum mechanics took off. The series ...


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No, you cannot hear the shape of the drum. Even if you have a list of the eigenvalues of the Hamiltonian, you cannot reconstruct the Hamiltonian. For example, these two Hamiltonians have the same eigenvalues: The spectral line is the same for both systems. Assuming that the transition is from energy 2 to energy 1, the first system goes from a state that ...


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In practice it would be very difficult to truly reconstruct "the" wave-function from the spectra. For one thing: Which wave function? Measured spectral emission/absorption are the result of transitions between states (ground and excited, e.g.) and these states all have their own wavefunctions. Furthermore, a typical measured spectrum is measured over a ...


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Boy, that term gets thrown around in a number of ways. In a MC generator context it sometimes means "everything but radiative corrections", but I don't know if that is the way the authors of Pythia mean it. On that assumption a "second hard process" would be a final state interaction that is modeled separately of the corrections; re-scattering in a ...


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I like Bill Gibbs' book Computation In Modern Physics for a couple of reasons (aside from having taken the course from the author): After introducing basic tools (difference approximations to differential equations, numeric quadratures (i.e. integrals), and eigenvalue problems in a matrix form) it moves right on to problems of interest to me. The examples ...


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For two bodies this is relatively easy as the equations of motion describe a conic (an ellipse for a closed orbit, a hyperbola for an "open" orbit). You can use the vis viva equation to get the parameters of the orbit (semi major axis etc) from the given initial conditions, and the rest follows. For an ellipse, you can also express the position as a ...


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Rather than leave these as comments, I guess I should answer it since this has come up before. A 2D simulation does not mean there is no third dimension. Rather, it means we are saying there is no variation in the third dimension such that $\frac{\partial}{\partial z} = 0$. But that depth direction still exists and we typically just call it a "unit depth" ...


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Answering my own question: it seems as if ISO 9613 might be the best way to accomplish this. In it, an algebraic methodology for calculating ground attenuation based on average heights AGL from source to receiver is given. Comparisons of this methodology with measurements and more complex PE solvers can also be easily found in literature.



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