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    Nuclear Physics - Uranium decay chain and Bateman equation

    Homework Statement Calculate the activity of ##^{222}Rn## in an ore sample containing 5g of natural uranium. Homework Equations ##^{238}U## decay chain (to Radon): ##^{238}U\rightarrow^{234}Th\rightarrow^{234}Pa\rightarrow^{234}U\rightarrow^{230}Th\rightarrow^{226}Ra\rightarrow^{222}Ra##...
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    Changing the basis of Pauli spin matrices

    Thanks! This yields the answer I got doing it the above way but is much more satisfying. I didn't even think of solving the matrix elements individually like that for some reason. Quantum mechanical problem solving simply doesn't adhere to the same intuition as other problems in physics. I can...
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    Changing the basis of Pauli spin matrices

    After some thought, I've considered that maybe I can just use the vector representation of S_z kets in the S_x basis. That is, |+>_x \doteq \begin{pmatrix} 1\\ 0 \end{pmatrix} in the S_x basis, and the same for the spin down ket, so I can just plug these vector representations...
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    Changing the basis of Pauli spin matrices

    Homework Statement Find the matrix representation of S_z in the S_x basis for spin 1/2. Homework Equations I have the Pauli matrices, and I also have the respective kets derived in each basis. There aren't really any relevant equations, other than the eigenvalue equations for the...
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    An optics problem - elliptical lens and plane waves

    Pergradus did you ever solve this problem and if so how
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