Recent content by hilbert2

Actually now that makes sense to me, even if a whole spherical surface acts as a delta potential, the particle will escape. Maybe it's a different situation if there's an infinite number of shells at ##r=R##, ##r=2R##, ##r=3R## and so on. Or a 3D lattice with point interactions at each lattice...

Yes, but only if it has a negative multiplier in front of it.

Suppose I have a 3D polyhedron with a large number of faces, and put a repulsing Dirac delta potential, ##c\delta (\mathbf{x} - \mathbf{x}_i )## with ##c>0## at each vertex point ##\mathbf{x}_i## of the polyhedron. Could this kind of an arrangement of delta potentials keep a particle such as an...

Yes, if you initially have two noninteracting hydrogen atoms, neither electron is likely to be at a large distance from the proton it orbits, so there is entanglement within each atom (but not necessarily in the spin variables that the concept of entanglement is usually demonstrated with). After...

I think it would be more difficult to entangle a 3rd particle with two entangled particles and also completely break the entanglement between the initial two particles. At least if there is no large number of other particles present in the interaction that you do this with.

Maybe it's also possible that some exotic particle in high-energy physics can absorb a photon to become a higher-mass particle without the KE or PE changing?

This equation also has the property that there is an infinite number of solutions only when ##c=0## or ##c=\pm 1## (can you prove this formally with mathematical induction or by some other way?).

The easiest way is to just set ##a=c## and ##n=1##.

That delta function potential is like the limit of a finite square well, ##V(x) = -V_0## when ##|x|<L/2## and ##V(x) = 0## when ##|x|\geq L/2##, if you start making it more narrow by decreasing ##L## and increasing ##V_0## at the same time so that the product ##V_0 L## stays at constant value...

Maybe what they here write about: https://www.sciencedirect.com/science/article/abs/pii/S0096300306015712 Basically, if you want an approximation for the roots of a polynomial, you find another polynomial where the coefficients of terms are similar enough in value and which has exactly...

I'm mostly considering a situation where two molecules approach along a straight line with fixed orientation (rotation angle). The system with a muon version of ##He_{2}^{2+}## as a "nucleus" and two electrons orbiting it is likely to be easy to calculate a ground state and equilibrium bond...

It doesn't, but if you calculate the average state(wavefunction) on the time interval ##[t_0 , t_0 + \Delta t]## and have a good enough guess for ##E_0##, you can set the value of ##\Delta t## to about half of the value needed for ##e^{-iE_0 t/\hbar}## to go one circle around the origin of...

An idea I was thinking about for the last few days: You want to calculate the ground state of some system from the Schrödinger eqn ##\hat{H}\left|\psi\right.\rangle = E\left|\psi\right.\rangle##. One way is to choose a trial state ##\left|\psi (t_0 )\right.\rangle## and use the TDSE to...

Thanks for the answer. The first what I going to say was that maybe the muonic helium atom, with a muon replacing one of the electrons, can also have that kind of a pair interaction potential because the muon in that atom is much closer to the nucleus than the electron. But the article you...

Pair interactions between atoms and molecules (in gas kinetic theory simulations or other applications) are described by empirical potential energy functions such as the Lennard-Jones potential: ##V_{LJ} (r) = 4\epsilon \left[ \left(\frac{\sigma}{r} \right)^{12} -...