Why not add non-toxic and non-polluting, while you're at it.
If there was such a chemical, you can be sure someone would be getting fifty rich right now by producing it.
And why shy away from carbon compounds? The problem wrt climate change is fossil fuels. If you could make fuel using...
You missed an i in the exponential.
https://en.wikipedia.org/wiki/Euler%27s_formula
I'm not sure that this answers your question, but as you wrote, to general solution is a sum of a sine and a cosine. There can be combined into a phase-shifted cosine or sine. By convention, most of the time...
Once you have the eigenvalues, you put them back in the eigenequation and solve for the coefficients of the eigenvectors ##(c_1, c_2)^T##. Note that the solution is not unique, so you can either solve simultaneously the normalization equation ##|c_1|^2 + |c_2|^2 = 1## or take arbitrarily ##c_1...
Sorry, I hadn't paid attention to the particular wave function you were working with. (There is a typo in what you wrote: it should be ##d^2/dx^2##.) I was answering the second part of
As for the first part, there is a typo in the answer. Norm is conserved and the normalization factor remains...
This is incorrect. The actual equation (for a time-independent Hamiltonian) is
$$\psi \left ( x, t \right ) = e^{-i \hat{H} t/\hbar} \psi \left ( x,0 \right )$$
It is only in the case where the exponential of the operator is acting on an eigenstate of that operator that you can replace the...
Go to the proper forum: for questions related to a specific exercise/problem, go to the appropriate Homework Help forum (e.g., Introductory Physics Homework Help). For more general questions, find the forum that covers the subfield of physics or another science (e.g., Classical Physics). In the...
The problem is that the second argument in JacobiSN and JacobiDN is ##m##, not ##k## (##k = \sqrt{m}##).
See
https://www.johndcook.com/blog/2018/10/12/jacobi-function-nomenclature/
It is whatever electromagnetic noise there is at the frequency of the channel. That noise will vary from channel to channel and from one location to another.
You should be able to answer the question without knowing the melting point of the material being heated.
That's it. If the iron is just starting to glow at 700 nm, then the peak wavelength must still be in the infra-red, so T < 4140 K.
What are the initial conditions?
For "fun," I implemented the Duffing oscillator in C using RKF45 from GSL, which should be the same integrator as the one used by Matlab, and I get the correct solution for the undamped case.
That's incorrect. The Fermi temperature is simply the conversion of the Fermi energy to units of temperature, with the Fermi energy based on the T = 0 distribution of fermions (degenerate Fermi gas). It is not the temperature at which the "lowest energy state" is attained.
The usefulness of...
For an isolated atom/molecule, there is no way to couple the internal and external degrees of freedom. In other words, there is no mechanism that would convert kinetic energy to, e.g., electronic or vibrational energy. Therefore, it is not possible to make atoms "glow" by accelerating them...
I'll explain later, after @warhammer has had time to work the problem.
I think you have to think about all that is happening, not just plug-and-play with the equation.
The trick is to embed BB codes such that $$ is not interpreted as the equation delimiter. In this example, I put color tags around the second $ (choosing black, so the effect is invisible).