I was doing some computational one-dimensional QM to time evolve an initial state by diagonalizing the hamiltonian and throwing it in an exponential, but I had initially forgot to include the eigenvalue matrices in my code, instead just including the diagonlized hamiltonian
however, once I fixed it I got nearly exactly the same time-evolved state, which I'm guessing is probably due to some obvious property of the system I was solving that is not so obvious to me
So why do gravitational waves travel at the speed of light? If they are the distortion of space, shouldn't they travel with the expansion of space on a comoving coordinate system?
In quantum mechanics, the unitary time translation operator $\hat{U}(t_1,t_2)$ is defined by $\hat{U}(t_1,t_2)|ψ(t_1)\rangle = |ψ(t_2)\rangle$, and the Hamiltonian operator $\hat{H}(t)$ is defined as the limit of $i\hbar\frac{\hat{U}(t,t+\Delta t)-1}{\Delta t}$ as $\Delta t$ goes to 0. Similarl...
@rob Hmm...another way to put it, why can't gravitational waves travel faster than light, if objects can recede faster than light due to the expansion of space?
@SirCumference Gravitational waves, like light waves, are a local phenomenon.
There certainly are distant galaxies for which the Hubble flow rate is larger than the speed of light. But the light from them that we see has traveled at $c$ through all the intervening space.
Gravitational waves travel the same way. The gravitational curvature is a property of the local vacuum, like the electromagnetic field is.
I feel like the god of LaTeX whenever I get a table right and y'all are doing animated movies in it, holy shit
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So, there's this heater in my room, and the piping really looked like gas piping, but it was warm so I didn't want to turn it on and find out. I spent a few days theorising in my head how it worked with some catalyst or something since it didn't have any sort of fire in it's functionality. Turns out it's just piped hot water with a heatsink and I lost some days of thought
@rob Question, if I have a 488nm wavelngth radiation, it's energy will be given by $E=\frac{hc}{488}$, right?
The actual problem is: "Determine the wavelength of the photoelectrons removed from a rhodium anion (Rh-) with a radiation of 488nm, knowing that the electroaffinity of Rh is 110,27 kJ/mol"
@rob "the electron affinity of an atom or molecule is defined as the amount of energy released or spent when an electron is added to a neutral atom or molecule in the gaseous state to form a negative ion"
Oh, it's for making negative ions. Ionization energy is for making positive ions, and work function is for removing a conduction electron from a metal.
@SirCumference So, convert your electroaffinity for a mole of negative rhodium ions (serious, wtf chemists) to find the energy associated with making a single ion.
"Ionization energy: the energy required to remove an electron from a neutral atom. Electron affinity: the energy change when a neutral atom attracts an electron to become a negative ion."
@BernardMeurer I want to know what it means by "with a radiation of 488nm"
In quantum mechanics, the unitary time translation operator $\hat{U}(t_1,t_2)$ is defined by $\hat{U}(t_1,t_2)|ψ(t_1)\rangle = |ψ(t_2)\rangle$, and the Hamiltonian operator $\hat{H}(t)$ is defined as the limit of $i\hbar\frac{\hat{U}(t,t+\Delta t)-1}{\Delta t}$ as $\Delta t$ goes to 0. Similarl...
