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I have one possible explaination. I used the infinite square well Hamiltonian (I didn't pay attention to boundary condititions since it will not matter for the big picture). Then I calculated the eigenvectors/eigenvalues in Mathematica. n = 50; d = KroneckerDelta; H = -Table[d[Abs[i - j] - 1] - 2 d[i - j], {i, 1, n}, {j, 1, n}]; v = Eigenvectors@H; e = ...


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In theory you could do this for any half cycle of the cosine. The derivative gives you v as a function of t. Solve the position equation for t as a function of x. Then use that t in the velocity formula. The problem is solving for t. Depending on why you need this, and the accuracy you need, you might use numerical methods. Choose an x. Goal Seek or ...


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I have to make a number of assumptions, as you did not state all the necessary information. So, I am going to assume that you are using periodic boundary conditions, that is, your Hamiltonian is $$ \mathcal{H}(\sigma) = -\sum_{i=1}^N \sigma_i\sigma_{i+1}, $$ where I have denoted by $N$ the number of spins (that is, $N=40$ in your case) and used the ...


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Choose a basis. Write the Hamiltonian matrix in that basis (e.g. like it's done here.) Diagonalise the Hamiltonian. That will give you the eigenenergies and energy wavefunctions. On Mathematica, for instance, you'd use Eigensystem.


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Transit of the probe at (near-)relativistic speed doesn't require much more than SR. The need for GR is less about speed and more about spacetime curvature. GR would have more relevance for propagating the planetary orbits (remember that historic observations of such were how the need for it was first suggested), but there is not going to be much more ...


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I would assume that using a slight variant of the restricted three-body problem would give a reasonable solution. Basically, the probe is the only truly relativistic object in the system, and its mass is sufficiently small that we could treat it as a "test particle". This means that the following technique would (I suspect) give a reasonable ...


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(a) I don't quite understand what you mean by the $\rho$ operator acting on $\left| k \right\rangle$, but the free evolution operator $U_{free} = \exp [-i T \hat{p}^2 / 2m]$ acting on $\left| k \right\rangle$ just tags the basis-ket with a phase factor. Therefore, $U_{free}\left| k \right\rangle = \exp [-i T k^2 / 2m]\left| k \right\rangle$ (b)If you apply ...


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Kepler's First Law states that planets (or any orbiting body) will travel in an ellipse where the center object (in this case the Sun) is situated at the foci. This is exactly how eccentricity is defined. If $c$ is the distance between the Sun and the center of the ellipse, $a$ is the semi-major axis (the distance from Sun in the factsheet you posted) then ...


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If your incident wavefunction is $$\psi_i=\frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^\infty{A(k)e^{i(kx-\omega_kt)}dk},$$ the transmitted wavefunction is $$\psi_t=\frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^\infty{\alpha(k)A(k)e^{i(kx-\omega_kt)}dk}$$ where the transmission coefficient for an incident wave $e^{ikx}$ is $T(k)=|\alpha(k)|^2$. The transmission ...


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I am not sure why one would need a special GitHub for physicists -since usual GitHub serves the purpose quite well. I do agree though that in physics there is a tendency to keep hidden the code AND the data. In my opinion, this is a field-specific feature. For example, in biology the journals often require for the data to be published alongside the ...


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ITensor has many tutorials published here. Please let know if there's something more you'd need which lacks from this page.


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I am not sure if it is of use any more, but to me it seems like Nrotstar is New-rot_star. If you visit the file Lorene/Codes/Rot_star/README, there the variable rot_star is said to be obsolete and the user is suggested to use nrotstar instead.


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I recommend De Lange, O.L. and Pierrus, J., 2010. Solved problems in classical mechanics: Analytical and numerical solutions with comments. Oxford University Press It contains a mixture of theory and numerical exercices, and all the numerical stuff is done using Mathematica. The book contains multiple levels of exercices and detailed complete Mathematica ...


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I am not familiar with Mathematica, but I can give you an approach for solving basic mechanics problems: 1. Sketch the situation. 2. Put in vectors to represent each force. 3. Define your symbols on the sketch. 4. For each mass in the system, write a component force equation (ΣF = ma) for each dimension of motion. 5. If relevant, write a torque equation (...


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Assuming you are using a normal Monte Carlo algorithm, your measurements should not have a negative correlation, and it is probably due to noisy data. If you want to fit a linear curve I would recommmend to either run more simulations, in order to reduce noise, or you can restrict your data to the domain where the auto correlation is large enough to not be ...


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