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One potential example of an experimental system that has this type of Lorentzian "wavefunction" is cavity-enhanced parametric down conversion (PDC) photon sources. In this case it isn't the position wavefunction but the "wavefunction" in frequency space which is Lorentzian (more correctly the joint spectral intensity (JSI) of two photons is an Airy ...


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$\psi(x) = \frac{1}{\sqrt{1+x^2}}$ is a perfectly valid wavefunction. However, one cannot find the expected value of $\hat X$ in this state, because $\psi$ is not in the domain of the $\hat X$ operator. The appropriate domain on which $\hat X$ is self-adjoint is $$D_X:= \left\{\psi \in L^2(\mathbb R) \ \left| \ \int_\mathbb R |x \psi(x)|^2 dx < \infty\...


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In the post you mention there are some references. Also, they tackle your question about the interpretation of expected values. Nevertheless I think you are interestred in wavefunctions $\psi$ such that $\vert\psi\vert^2$ is a Lorentzian, which, you know, is not eactly the same! Edit: Sorry to say that Loretzian wave-function is not square integrable.


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You may want to consider using a suspended magnet attached to a mirror. A laser reflecting off of the mirror will detect the magnetic field produced by a AAA battery 12 feet away. Here’s a link to my video where I conducted this experiment. The portion related to your question starts a 9:33 into the video.Here it is.


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As a simple, but engaging alternative, you could try having them make their own homopolar motors with wire and a battery. As a starting point, Wikihow has some instructions on the basic set-up.


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When Michael Faraday made his discovery of electromagnetic induction in 1831, he hypothesized that a changing magnetic field is necessary to induce a current in a nearby circuit. To test his hypothesis he made a coil by wrapping a paper cylinder with wire. He connected the coil to a galvanometer, and then moved a magnet back and forth inside the ...


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What you are using is the Helene formula. (Also known as "the old PDG method"). It is the same as CLs when you are dealing with numbers of events (as you are here) rather than a likelihood analysis which also includes shape information. For the frequentist CL you use your Equation 1 without the denominator. The. modification is an attempt to include the ...


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After a long time both capacitors look like open circuits. That means there is no current flowing anywhere in the circuit. Like you stated all the battery voltage is across the left capacitor. Since no current is flowing in the resistor in parallel with the series combination of the right capacitor and its resistor, there is no voltage across them. The ...


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Assuming that the galvanometer has a coil in it then the effect is due to the relatively low total circuit resistance. What this means is that we are dealing with a spring-mass system which is massively over-damped. The mass is the coil and former and the spring is the return spring(s) which moves the coil to the equilibrium position when there is no ...


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If you look at the particle data group tables, mesons for example you will see for each resonance listed its parity, in the same line as the name and the mass of the resonance. Like the mass, it is an observation from measuring the resonance in experiments, laboriously in experiments over the years . for example, the parity of the pi- was measured in a ...


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How is the counting-rate of particles obtained in an experiment? It depends on the experimental setup. Experiments measure neutrino oscillations by starting with a known neutrino beam, measuring its content in the three standard model neutrinos, i.e. have detectors that count how many there are at one specific location, then put a detector far enough ...


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Based on the comments, the mass in boxes $B_2$ and $B_3$ is not uniformly distributed throughout the box, whereas it is in box $B_1$. This means that the inertia tensor for boxes $B_2$ and $B_3$ will be different than the inertia tensor for box $B_1$; the inertia tensor can be discovered experimentally by applying a known torque for a set time on a few ...


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The trouble with this question is that there is no strictly objective answer... only time will tell. How would we ever know what there is left to be discovered in any situation? Only after making a discovery do we know that there was one to be made in the first place... We have a Standard Model of Particle Physics that describes existing measurements very ...


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Just to add a bit on the second point: However, in my case, I just have a number of counts per bin. So if I just change the $x$-axis form wavelength to energy, the number of counts should not change. Therefore, I think that I should not rescale the $y$-axis when passing from wavelength to energy. To understand this a bit better, let's suppose that you ...


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I think the answer to your first question is that it depends on the principle of operation of the spectrometer. For example a Fourier Transform Spectrometer is basically just a Michelson interferometer, so one could argue that by creating interference patterns you are selecting a sample from a continuous spectra. On the other hand, if you have a grating ...


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You may want to go with D batteries. An old computer or stereo-amp that someone is throwing out may have a good multi-amp DC power supply. Some of the little black boxes (often available at garage sales) may be rated for 2 amps DC. Harbor Freight carries a low cost digital multi-meter. I use to string a wire from ceiling to floor next to a table. Boards on ...


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As I understand it, some experiments have been done in the past with negative results, or results that could not be duplicated. The consensus in the scientific community is gravitational shielding does not exist except in science fiction. It is considered to violate the equivalence principle making it inconsistent with both Newtonian theory and the theory of ...


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Why not use a plotting compass instead of a home-made magnetised needle? Plotting compasses are available from educational suppliers. They used to be very cheap. They are easy to use. With a current of 2 A through a long wire you should get a field of about 40 $\mu$T at 1 cm from the wire. This is of the same order as the Earth's magnetic field, so the ...


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A ferromagnetic material is made up of many small regions called “domains”. Often, each domain is a single crystal, and the atomic dipole moments tend to line up with the crystal axis. In an un-magnetized sample the crystals and dipole moments are randomly oriented giving a resultant field of zero. If placed in an external magnetic field, the dipoles in ...


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Maybe the helium and neon could get ionized and form some molecules not normally possible. Maybe neon could rain down and form molecules under really special circumstances. Maybe ionic version of neon could bond with other elements and instead of being atomic like it normally is it could be molecular and maybe this molecule could rain down to the surface. If ...


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I don't know if this counts as an answer, but $\frac{dN}{dt} \propto N \Leftrightarrow N(t) = N_0 e^{-t/\tau}$. This is a mathematical equivalence. So instead of plotting $\frac{dN}{dt}$ vs $N$, you could just plot $\log \left(\frac{dN}{dt} \right)$ vs $t$ and check that it follows a straight line.


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I'm guessing: Start with a pure sample of your isotope. After some time, do a chemical (or physical) separation of the isotope and the decay product. Then weigh them separately.


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Newtonian gravity is said to be universal. However when they mean universal they mean it is mostly universal. There are times when it does not work. For example in the Big Bang or near or even inside a black hole(even general relativity does not work in the inside of a black hole). When things get really small or really big there is a possibility that ...


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This is not really possible to check experimentally. In order to experimentally check that a function is continuous, you would have to be able to make measurements that are infinitely close together, which isn't possible.


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