Recent content by AndersF

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    Dependence of the stress vector on surface orientation

    According to Cauchy's stress theorem, the stress vector ##\mathbf{T}^{(\mathbf{n})}## at any point P in a continuum medium associated with a plane with normal unit vector n can be expressed as a function of the stress vectors on the planes perpendicular to the coordinate axes, i.e., in terms of...
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    I Problem involving a sequential Stern-Gerlach experiment

    Well, with the answers I have read, I think I have managed to clarify myself with this topic (also, looking at vanhees71's articles, it seems that the topic is extensive). Thank you very much :)
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    I Problem involving a sequential Stern-Gerlach experiment

    Rather than a book, I should have said notes, it's a text written by the professors for the Quantum Mechanics course I am taking (and not a very good one, by the way). I'm sorry, I don't have more information...
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    I Problem involving a sequential Stern-Gerlach experiment

    The statement of the problem doesn't specify it. I guess that Demystifier is right and that there are two second SG magnets.
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    I Problem involving a sequential Stern-Gerlach experiment

    Yes, the first beam splits in two after passing through the first S-G, and then both beams pass through the second S-G.
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    I Problem involving a sequential Stern-Gerlach experiment

    An electron beam with the spin state ## |\psi\rangle = \frac{1}{\sqrt{3}}|+\rangle+\sqrt{\frac{2}{3}}|-\rangle##, where ##\{|+\rangle,|-\rangle\}## is the eigenstates of ##\hat S_z##, passes through a Stern-Gerlach device with the magnetic field oriented in the ##Z## axis. Afterwards, it goes...
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    I Parallel transport of a tensor

    Oh ok, it is by far much clearer the way you wrote it. Now I see it, thanks!
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    I Parallel transport of a tensor

    According to my book, the equation that should meet a vector ##\mathbf{v}=v^i\mathbf{e}_i## in order to be parallel-transported in a manifold is: ##v_{, j}^{i}+v^{k} \Gamma_{k j}^{i}=0## Where ##v_{, j}^i## stands for ##\partial{v^i}{\partial y^j}##, that is, the partial derivative of the...
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    I Showing that the determinant of the metric tensor is a tensor density

    Ok, these were just the "tricks" I was looking for, thank you very much!
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    I Derivation of the contravariant form for the Levi-Civita tensor

    The covariant form for the Levi-Civita is defined as ##\varepsilon_{i,j,k}:=\sqrt{g}\epsilon_{i,j,k}##. I want to show from this definition that it's contravariant form is given by ##\varepsilon^{i,j,k}=\frac{1}{\sqrt{g}}\epsilon^{i,j,k}##. My attempt What I have tried is to express this...
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    I Showing that the determinant of the metric tensor is a tensor density

    I'm trying to show that the determinant ##g \equiv \det(g_{ij})## of the metric tensor is a tensor density. Therefore, in order to do that, I need to show that the determinant of the metric tensor in the new basis, ##g'##, would be given by...
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    I Doubt about the purpose of some elements in tensor calculus

    Okay, thank you very much, I have found your answers very helpful :)
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    I Doubt about the purpose of some elements in tensor calculus

    I would like to know what is the utility or purpose for which the elements below were defined in the Tensor Calculus. They are things that I think I understand how they work, but whose purpose I do not see clearly, so I would appreciate if someone could give me some clue about it. Tensors. As...
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    I Expressing the vectors of the dual basis with the metric tensor

    Okay, thanks, I see that it was the notation that confused me.
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    I Expressing the vectors of the dual basis with the metric tensor

    Oh, why not? They are written like this in my textbook
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