Coulomb potential Definition and 25 Threads

Consider a scenario in the picture where one half of space consists of a material with permittivity ϵ1 and the other half consists of a material with permittivity ϵ2, where ϵ1 > ϵ2. A unit positive charge is fixed at the interface between the two materials. Path1 is entirely within the material...

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they...

$$\bar u(p') \gamma^i u(p) = u^\dagger(p') \gamma^0 \gamma^i u(p)$$ if ##p = p'## we can use $$u^\dagger(p) u(p) = 2m \xi^\dagger \xi$$ but how can we conclude the statement?

I am struggling over a problem and i could really use some help in this. So it's about finding phase shifts in a localized sphere of coulomb and harmonic potential. I tried solving the radial Schrodinger equation for both of them by using power series method, but still i am having problem...

Hi, I have a question about calculating probabilities in situations where a particle experiences a sudden change in potential, in the case where both potentials are time independent. For example, a tritium atom undergoing spontaneous beta decay, and turning into a Helium-3 ion. The orbital...

Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...

As I understand Coulomb potential associated with charged particle is described classically. My question is if there is a way how to describe Coulomb potential of charged particle that is in quantum superposition of being "here" and "there"? My motivation for question is that I am trying to...

Dear all, In my quantum mechanics book it is stated that the Fourier transform of the Coulomb potential $$\frac{e^2}{4\pi\epsilon_0 r}$$ results in $$\frac{e^2}{\epsilon_0 q^2}$$ Where ##r## is the distance between the electrons and ##q## is the difference in wave vectors. What confuses me...

Hello everyone Homework Statement I have been given the testfunction \phi(\alpha, r)=\sqrt{(\frac{\alpha^3}{\pi})}exp(-\alpha r) , and the potential V(r,\theta, \phi)=V(r)=-\frac{e^2}{r}exp(\frac{-r}{a}) Given that I have to write down the hamiltonian (in spherical coordinates I assume), and...

I want to calculate the commutator ##{\Large [p_i,\frac{x_j}{r}]}## but I have no idea how I should work with the operator ##{\Large\frac{x_j}{r} }##. Is it ## x_j \frac 1 r ## or ## \frac 1 r x_j ##? Or these two are equal? How can I calculate ##{\Large [p_i,\frac 1 r]}##? Thanks

In chapter 4 of "Modern Quantum Mechanics" by Sakurai, in the section where the SO(4) symmetry in Coulomb potential is discussed, the following commutation relations are given: ## [L_i,L_j]=i\hbar \varepsilon_{ijk} L_k## ## [M_i,L_j]=i\hbar \varepsilon_{ijk}M_k## ## [M_i,M_j]=-i\hbar...

I'm seeing a version of the potential as -Ze^2/4πεr. My question is what exactly does the Ze^2 refer to? I think the e^2 is supposed to represent the proton and the neutron, and the Z is supposed to represent the number of protons, but I'm not sure how to read it. Does e refer to the charge...

Consider the potential below: V(x)=\left\{ \begin{array}{cc} -\frac{e^2}{4\pi\varepsilon_0 x} &x>0 \\ \infty &x\leq 0 \end{array} \right. The time independent Schrodinger equation becomes: \frac{d^2X}{dx^2}=-\frac{2m}{\hbar^2} (E+\frac{e^2}{4\pi\varepsilon_0 x})X I want to find the ground...

In Kohn-Sham DFT, the Coulomb potential, which is a component of the Kohn-Sham potential, is given by: v_H(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'} where \rho(\mathbf{r'}) is the electron density. For molecular systems with exponential densities...

Hi, I need a formulation of the equation for Coulomb's potential. It needs to be an integral that applies to densities (so no delta functions). (I think the relevant densities are charge densities?) Also, it needs to be relativistic. So far I have: ? = \int\frac{ρ(r'...

is it just potential and potential energy? but if so, why is it given as V(r) = - Ze2 / 4πεr ? and E = Z2e2 / 4πεr i am having trouble understanding how come for potential V, Q = Ze2 while for E, Q2 = Z2e2 thanks!

I have seen the Fourier transform of the coulomb potential quite often. However, I have come across a sum expression for an electrostatic potential V_{cb}(r-r') = \frac{1}{V}\sum_{q \neq 0} \frac{4\pi}{q^2}e^{iq(r-r')} It is equation (2.6) here...

Homework Statement Show that the expectation value of the Coulomb potential v(\vec{r_1},\vec{r_2})=\frac{e^2}{|\vec{r_1}-\vec{r_2}|}, between two electrons depends on the relative orientation of spin of the two electrons. Assume each electron is in the product state form...

Is there a general analytic solution to the classical motion of a relativistic charged particle in a static Coulomb potential? Of course, the non-relativistic limit is simply Kepler's problem. Quantum effects should be ignored, but relativistic effects (such as E field transforming into B field)...

The Coulomb potential energy between two point charges is defined as: V=[(q_1)(q_2)]/[(k*r)] Suppose that you have two equal, like charges at a distance L, then V_like=q2/(k*L) Similarly, for two equal, opposite charges, V_opp=-q2/(k*L)=-V_like Both situations experience a force of...

Hi every one this is the first time in this wonderful forum :) and i have a question i hope i find an answer ? how can the additiona of a smalll (c/r square)term to the coulomb potential removes the degnerecay of states with different (small) L. (quantum defect)? :confused: thanks

Homework Statement There is a propagating planar wave of the Coulomb potential, \phi = sin(kx - \omega t) . What other fields result when it is assume the magnetic potential, \textbf{A} is everywhere constant? \phi, Coulomb potential \textbf{B}, magnetic field strength \textbf{E}...

If I describe a system by a Lagrange's function L=-\frac{1}{2}\int d^3x\;(\partial_{\mu}A_{\nu}(x))(\partial^{\mu} A^{\nu}(x)) - \sum_{k=1}^N \Big(q_k A^0(x_k) - q_k v_k\cdot A(x_k) + m_k\sqrt{1-|v_k|^2}\Big) (I'm just coping this from my notes. I'm sure the not gauge fixing Lagrangian with...

The Coulomb potential barrier of a system of two nuclei X and Y is approximately given by VC = ZX*ZY*e2/RN where ZX and ZY are the charge numbers of the nuclei, e2 = 1.44 MeV*fm, RN = (AX1/3+AY1/3) × r0 is the sum of the nuclear radii. r0 is a constant usually estimated to 1.2 to 1.3 fm and AX...

I've seen the Fourier representation of the Coulomb potential is -\frac {Ze} {|\mathbf{x}|} = -Ze 4\pi \int \frac {d^3q} {(2\pi)^3} \frac {1} { |\mathbf{q}|^2} e^{i\mathbf{q}\cdot\mathbf{x}} Will anyone show me how to prove it? (yes, it's the Coulomb potential around an atomic nucleus.)...