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As for the second question, it's fairly simple. For a vertically emitted electron, the horizontal (x-axis) momentum is zero. But, as stated, the horizontal momentum of an electron detected at the edge of the cone is $$p_x = \frac{H}{\lambda}\sin{\theta} = p\sin{\theta}$$ but keep in mind that is simply the maximum possible, since the electron can be ...

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I think we can divide most potential solutions into 3 broad categories depending on what sort of reference is used: Some property inherent to your body or brain: As mentioned in rob's answer, the most obvious is probably to use one of several second counting methods, or a song, drum beat or similar that you have experience performing at a fixed pace. Some ...

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If your hypothetical stranded astronaut is able to use her own head-to-sole height as a length reference, I would expect her to count seconds by muttering "mississippi one, mississippi two, mississippi three" the way she has been doing since playground days. If your astronaut is a musician she might recall a piece of music for which she knows the ...

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You've stated that you'd recreate an SI length unit $\text{m}$ (meter) from knowledge of your own height. So you've got a reasonably accurate ruler. Create a small angle pendulum with length $L$. Use this clock to measure the speed of light (in vacuum). Call this $c_p$ (measured with the planet's pendulum period). The ratio of $c$ (measured in SI units ...

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The trick to exponentiate the $2\times 2$ matrix is to diagonalise it. A diagonal matrix $D$ exists such that $H= C^{t}DC$, with $C$ being orthogonal due to the fact that $H$ is hermitian. Using the orthogonality of $C$ and the definition of the exponential as power series leads you to prove that $$e^{-iHt} = e^{-i(C^{t}DC)t} = C^{t}\,e^{-i(D)t}\,C$$ and ...

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The uncertainty principle of quantum mechanics is neither a statement about Fourier transforms, nor is it a statement about the "precision" of measurements as such (although the experimental measurement of the standard deviation is of course only accessible by repeated experiments). For any quantum state $\lvert \psi \rangle$ and any observable $A$, we ...

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It is wrong to describe the equipment as "faulty" . It is just different and when you carry out the experiment with the "different" equipment you will get a different answer.The scientific method requires that experiments be repeatable.So if you can repeat the experiment with the "faulty" equipment then you have just carried out a new experiment.

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Imagine a simpler set up. You have a double slit and you purchase a super fancy which way device and out it next to the left slit. But you forget to remove the wrapper it came with. So it just goes off randomly at random times based on some thermal properties of say the wall current you plug it into. You might incorrectly think that almost all the ...

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