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17

In the lab frame there is a magnetic attraction, but it will never overpower the Coulomb repulsion between the two beams. This is easiest to see in a frame of reference which moves with the electrons themselves: there, the electrons are stationary, and the only force between them is the repulsive Coulomb force. That said, if the electrons are moving fast ...

8

The classical electromagnetic waves as modeled by Maxwell's equations solutions, are one framework, the classical one. Electrons and photons are elementary particles and are in the quantum mechanical framework. The classical framework, emerges smoothly from the quantum framework at the overlap kinematic regions. One cannot use the same mathematics without ...

7

I suspect you are relying on the modern language, which is yet controverted by the effective theory community these days, if I am not too cut off from recent developments... I believe it is all hiding behind the receding obsession with renormalizability, and thus minimal coupling, obviated by the Wilson revolution. The point is the minimal-coupling ...

5

Because you haven't given us any information about the initial distribution of the charge within the cloud, I will assume here that the distribution is uniform (specifically, $\rho(r)=\rho_0$ for $r<r_0$ and $\rho(r)=0$ otherwise). Importantly, that means that the problem has spherical symmetry. Since the cloud is spherically-symmetric, the electric ...

4

You can do the do the whole derivation using quantum mechanics (see for example J. M. Ziman's Electrons and Phonons section 1.3. His Principles of the Theory of Solids probably does the same thing.), and you get the same result. In fact, the derivation looks basically the same. When you treat the atoms as though they're connected by springs, this simply ...

3

Lets start with the basic definitions: The elementary charge, usually denoted by e or sometimes $q_e$, is the electric charge carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −1 e Charge is a quantity measured in the laboratory, and in coulombs, is $1.60217662 × 10^{-19}$ ...

2

The existence of a minimum energy follows from the wave-like aspects of matter. The allowed values of energy are those corresponding to stationary wave states, so the trite answer to your question is that where you have a set of allowed energy values one of them has to be a minimum. To get some physical insight into why the minimum level ends up where it ...

2

Yes, there is Coulomb interaction, which also leads to correlation in position. As an example, you could look at helium. The binding energy of one electron is 4 Rydberg = 54.4 eV. But the ionization energy of neutral helium is 24.6 eV. Calculating this number is not so easy because it is a three-body problem. One way of taking into account electron-...

2

Loosely speaking, yes. By 'feel each other's Coulomb potential' you mean that the behaviour of one electron is influenced by the presence of the other owing to electrodynamic effects. That is undoubtedly the case. If you were to model the behaviour of an electron in an atom by considering only the potential due to the nucleus and electrons in other orbitals ...

2

If you look at the problem in the electrons' stationary reference frame, where there is only a Coulomb force and no magnetic field, then you can see that there is always repulsion between the electron beams. All observers in other reference frames will agree that there is a repulsive force between the electron beams, but in the stationary lab frame, the ...

2

when it is being deformed in the hot press, the atoms in its lattice are being pushed past one another, and the solid metal flows like stiff taffy. The slag on the outside is brittle, and when it exfoliates, a fresh new red-hot iron surface is exposed to air. It violently oxidizes, producing flames and sparks. Each time the ingot is deformed more, the ...

2

The presence of $r$ in the formula you used implies that it is based a contact scattering assumption. That kind of assumption makes sense for modeling the atoms and molecules of a neutral gas or neutron diffusion, but it doesn’t make sense for modeling the interactions of charged particles unless you tunes the radius you use to express the median impact ...

2

Electrons and photons are quantum mechanical entities, obeying quantum mechanical equations. What you are describing with words is a classical description of light which is controlled by classical electrodynamic equations, Maxwell equations. An accelerating charged particle produces an electromagnetic (EM) wave. Electromagnetic waves are electric and ...

2

There are a few ways to create photons: accelerating charges (like in your example), but based on the comments, you need to count accelerating magnetic dipoles too. https://physics.stackexchange.com/a/65350/132371 electron relaxation, that is when an excited electron as per QM at a higher energy level moves to a lower energy level, and the difference in ...

2

You don't need to go all the way into quantum mechanics to understand what's meant for "light frequency". Classically, light is energy being transported by the electromagnetic (EM) field. When the electron vibrates it modifies the EM field in such a way that energy propagates away. This field is a vector field, that means for every point in space the EM ...

2

How can the annihilation of an electron and a positron create a quark-antiquark pair or a muon-anti muon pair? .... But the total rest energy of the electron and positron(1.102 Mev) is less than the the total energy required to produce either the quark-antiquark pair or the muon-anti muon pair(211.4 Mev) Certainly if the annihilation happens at rest, i....

1

According to our currently accepted theory, the SM, electrons and quarks are elementary particles, pointlike, with zero spatial extension, and no substructure. Now what you are suggesting, that the electron and quarks are not elementary, not pointlike and they do have a substructure, and some spatial extension could be based on two theories: preons ...

1

In Quantum Mechanics, within the Copenhagen interpretation, the squared modulus of the wavefunction is associated to the probability of finding a particle in a certain position in space. Since, according to an axiomatic definition of probability, a correctly defined probability is normalized, in this case we can say that also the squared modulus of the ...

1

You are looking for a conceptual model that makes sense, so you want a classical explanation. Quantum explanations will not make sense that way. You have the fundamental ideas straight. Opposite charges attract, same charges repel. It's a force field. A moving charge has a different force from a charge with no relative motion -- the direction and intensity ...

1

I'll have a go at a hand-wavy explanation which assumes that you are comfortable with the idea of an electromagnetic field. If you're not, let me know and I'll address that in an edit. Light is ripples of electromagnetism. When people talk about the speed of light they mean how quickly the ripples travel through space. The frequency of light is the rate at ...

1

Sometimes QM gives exactly the same answers as Newtonian mechanics. In this case, the equation for the phonon can be quantized directly, and the "acoustic" sound wave field becomes the wavefunction of the phonon. If you want to discover this yourself, solve those equations and notice that they contain both positive and negative frequencies - sure sign that ...

1

The answer by cmaster is correct. As an example, consider the probability $|\psi(x)|^2$ of a superposition of the two lowest eigenstates of a particle in a box: That charge density is oscillating, sloshing back and forth in the box, with a frequency $\omega = (E_1-E_2)/\hbar$, which is the frequency of the emitted photon. While it is radiating, the ...

1

Let us be clear, acceleration , velocity, force are classical definitions. What exists in the quantum mechanical and, generally, quantum field theory is four vectors and interactions. It is simple to think of Feynman diagrams, which have a $\mathrm{d}p/\mathrm{d}t$ at each vertex, being given or taken away by the interaction, that is the connection with $F=... 1 As with a magnetic lens the electrostatic field between conducting electrodes is configured to produce a converging lens. Assume that it is positive changes which are being deflected an a very much idealised arrangement. The arrangement of three cylindrical conductors and their relative potentials, and the resulting electric field is shown as the top left ... 1 The scanning coils work in principle just like the deflection coils of a CRT ("fat TV" or analog oscilloscopes). They deflect the electron beam, making the focus move in a raster pattern over the sample. 1 To use a somewhat quantum fieldy but handwavy description (as would probably be enough in this context), the electron in the ground state behaves like an "antenna" for EM radiation of the correct wavelength. The resonance between the electron and the EM field allows it to absorb the photon and change its own wavefunction to the more energetic one ("go up"). ... 1 ...particles with the same quantum numbers cannot occupy the same space (pauli exclusion principle), while with different numbers such as spin they can. Does that mean the two electrons are invisible to each other<...>? No, this doesn't mean that they are invisible. It's just that Coulomb potential is a "soft" potential: due to Heisenberg uncertainty ... 1 You're right, and your book is wrong. The magnetic field is coming out of the page. The velocity vector of the electrons is to the right. The magnetic force acting on the electrons is$-e\textbf{v}\times\textbf{B}\$, which is up. The is contrary to the information stated in the quote in the book. The deflection should be up.

1

From: Carver Mead's "Collective Electrodynamics" Section Magnetic Interaction of Steady Currents 1.11 Current in a Wire Speaking of superconducting currents in a wire: At long last, we can visualize the current distribution within the a superconducting wire itself. Because the skin depth is so small, the surface of the wire appears flat on that scale, ...

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