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Let the magnetic field be in the $\hat z$ direction. If you calculate the expectation values of $S_x$ and $S_y$, you find that they have time dependence like $\cos(\omega t),\sin(\omega t)$ while the expectation value of $S_z$ is constant. Explicitly, the Hamiltonian is $H = -\omega \sigma_z$. Using the Heisenberg equation of motion, \begin{align} \dot ...


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As far as I know, the external magnetic field that produces a torque on the magnetic moment is not necessarily the reason for the precession of it around the direction of the magnetic field. The magnetic moment of an electron is proportional to it's spin and its revolving motion around the nucleus. so when an external field acts on it, it tends to align in ...


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Spontaneous emission and stimulated emission are cases related to measurement, but they are not identical to measurement. We might ask how the measurement of states and the preparation of states are related to measurement, or the decoherence of states. Both are necessary aspects of quantum physics. In order to do experiments we need to prepare identical ...


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Phenomena in quantum mechanics may be expressed using any basis. It doesn't mean that all bases are equally useful for a given situation. In particular, a fundamental postulate of quantum mechanics says that right after every measurement, the system is found in one of the eigenstates of the observable that was just measured. That's why the basis of the ...


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Take for example the double-slit experiment interpreted in the Copenhagen sense. The particle leaves as an object with mass, yet passes through the slits as a massless wave, only to collapse again as a particle. We can consider this example as a generalisation of the principle of anti-realism posited by Bohr. Where does the energy "go" when the ...


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Short answer: no. I'll give some context with the details of the simplest examples. In the context of conservation laws, "energy" refers to the Hamiltonian. In classical mechanics, a quantity without explicit time dependence is conserved iff its Poisson bracket with the Hamiltonian is 0. In quantum mechanics, quantities are promoted to operators on a ...


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OP explicitly asks whether a material object (i.e. not a state of light) has been placed in the superposition $|\psi⟩=|\psi_1⟩+|\psi_2⟩$, where $|\psi_n⟩$ is the $n$th Fock state of a harmonic oscillator. Perhaps the clearest example of this is the achievement of precisely that superposition in the quantum state of a cantilever microwave resonator ...


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I think Schrodinger's cat experiment is a word conundrum rather than reality. For example, it took 1000 years for philosophy to prove that a man could run faster than a tortoise. I.E., Achilles and the tortoise: In a race, the quickest runner can never overtake the slowest [if had a head start], since the pursuer must first reach the point whence the pursued ...


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Following Lubos' comments, it is clear that your problem is equivalent to two quantum computers exchanging signals (or equivalently, a single one with a halting state). If your question is: Will the simulated cat be "alive" (that is, enjoying his simulated life), or "dead" (that is, the computer has halted and the cat no longer experiencing a simulation) ...


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Weak measurements don't let you learn about the system without disturbing it. They let you make tradeoffs, where you disturb/decohere/collapse less by revealing less, but you still have to pay for whatever the measurements do reveal. You can't combine many weak measurements into a "free" strong measurement. But say Alice weakly measures X, and learns ...


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In quantum mechanics all predictions and descriptions of nature come with a probability distribution . A simple example are the orbitals of the hydrogen atom.. The probability for an electron to be found at (x,y,z,t) can be calculated and the result, is called an orbital, because it is not a classical orbit. To compare a probability distribution with the ...


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Is momentum of a particle "random" because it is uncertain, or is it uncertain in addition to being random? In quantum mechanics systems are represented using wave-functions (wave-vectors). The momentum of a particle is completely uncertain if it's position is certain (a localized particle) . But it is also possible to create wave-functions that have a ...


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A particle is a wave. It's wave function (consider non relativistic Quantum Mechanics), when absolute valued squared, is a probability density function. The particle's momentum is a multiple of the gradient of the wave function, with h, Planck's constant, one of the proportionality constants. That is then the probability density function for momentum. It is ...


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If we setup the camera to record like above but NEVER EVER EVER look at the result of what was recorded. Does the wave function still collapse? The answer is that we just don't know. We can tell that the wave function has collapsed (in Copenhagen terms) only when we humans look at the system -- in the canonical experiment that means looking at the ...


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Experimental determination of $c_i$ values starts with preparing multiple identical systems, then making measurements. From all the measurements, one determines the probabilities, which are the $|c_i|^2$. The square root of the probabilities will tell you the $c_i$ to within a phase factor of the form $e^{i\beta}$, where $\beta$ is real, and may or may not ...


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Once a measurement ( observation ) is made on a quantum system the system will be in an eigenstate of that property, so if the energy of an electron is measured the electron will afterwards remain in an energy eigenstate ( until some other measurement or interaction occurs ), but if the angular momentum is measured the electron system will afterwards remain ...


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I think you are probably misinterpreting the context here. If you read the previous line carefully it says "there is always an undetermined interaction between observer and observed; there is nothing we can do to avoid the interaction or to allow for it ahead of time. And later he just says due to the fact that photon can be scattered within the 2θ' angle ...



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