Ground state Definition and 275 Threads

Hi! 1. Homework Statement From the website http://www1.uprh.edu/rbaretti/MomentumspaceIntegration8feb2010.htm we can see the Fourier transform of the ground state hydrogenic wave function : Φ(p) = ∫ ∫ ∫ exp(-i p r) (Z3/π )1/2 exp(-Zr) sin(θ) dθ dφ r² dr (1.1) After intregation...

I'm trying to understand chapter 19 of these lecture notes. But I have some difficulties with what the author explains: 1) In page 176, under equation 19.3 he says: This is weird. If we are considering a local QFT, then how can he say IR physics can cause non-locality? What is he talking...

Homework Statement Hi everybody! I have a problem related to first-order perturbation theory, and I'm not sure I'm tackling the problem correctly. Here is the problem: Consider a hydrogen atom in an externally applied electric field ##\vec{F}##. Use first-order perturbation theory to find the...

Homework Statement A hydrogen atom transitions from ni= 5 state down to the ground state. a) What is the energy of photon emitted from the transition of the hydrogen atom? b) What is the ratio of the momentum of the emitted photon to the momentum of an electron which possesses the same kinetic...

I was reading Peskin&Schroeder's QFT book, and there was some discussion about how ##\left|0\right>##, the ground state of a free field and ##\left|\Omega \right>##, the ground state of an interacting field differ from each other, and they outlined how the latter can be obtained by propagating...

Homework Statement Using Hund's rules, find the ground state L, S and J of the following atoms: (a) fluorine, (b) magnesium, and (c) titanium. Homework Equations J = L + S The Attempt at a Solution I'm having trouble understanding what L, S and J mean on a basic level. I read the textbook...

From the path integral approach, we know that ## \displaystyle \langle x,t|x_i,0\rangle \propto \int_{\xi(0)=x_i}^{\xi(t_f)=x} D\xi(t) \ e^{iS[\xi]}##. Now, using ## |x,t\rangle=e^{-iHt}|x,0\rangle ##, ## |y\rangle\equiv |y,0\rangle ## and ## \sum_b |\phi_b\rangle\langle \phi_b|=1 ## where ## \{...

Homework Statement An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state. Homework Equations ##\psi _{0} =\left(...

I saw another post about this but i didn't quite find what i was looking for there so i thought i'd give it a go instead with a thread. Homework Statement Calculate the exact value of the kinetic energy of the hydrogen atom in its ground state. No more information is given, we are referred to...

Homework Statement Estimate the ground state energy (eV) for an exciton in Si. εSi = 12 ε = 1.0359×10−10 Effective masses me* = 0.26me mh* = 0.36me effective mass = 0.15me Values of h 6.626×10−34 J⋅s 4.136×10−15 eV⋅s Values of ħ Units 1.055×10−34 J⋅s 6.582×10−16 eV⋅s Homework Equations E1 =...

Do all electrons orbit in the ground state, when the band gap, is increased, or decreased, as atoms come together to form molecules.? Like in glass, transparent liquids, and plastics. As atoms come together to form glass, like silicon, sodium, and calcium. Do the electrons orbital permanently...

Homework Statement Consider a quantum particle of mass m in one dimension in an infinite potential well , i.e V(x) = 0 for -a/2 < x < a/2 , and V(x) =∞ for |x| ≥ a/2 . A small perturbation V'(x) =2ε|x|/a , is added. The change in the ground state energy to O(ε) is: Homework Equations The...

What do you think about Feynman's description (http://feynmanlectures.caltech.edu/III_12.html#Ch12-S3) ? It seems to be inconsistent with hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html).

How to compare the ground state energies if diagrams containing x vs V are given. I saw a problem containing diagrams three potentials and they have asked to arrange them in order of their ground state energies. One was a potential well, and the other two had small perturbation in the middle...

I have the solution for this problem but don't understand it. 1. Homework Statement Use Hund's rules to calculate the ground state of erbium with electron configuration [Xe]4f126s2 Homework Equations Hunds Rules: 1. Maximise S (within Pauli) 2. Maximise L (within Pauli) 3. Min J (for...

For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?

I am trying to perform the operation a on a translated Gaussian, ie. the ground state of the simple harmonic oscillator (for which the ground state eigenfunction is e^-((x/xNot)^2). First, I was able to confirm just fine that a acting on phi-ground(x) = 0. But when translating by xNot, so a...

Homework Statement a particle of mass m moves in 1D potential V(x),which vanishes at infinity. Ground state eigenfunction is ψ(x) = A sech(λx), A and λ are constants. find the ground state energy eigenvalue of this system. ans: -ħ^2*λ^2/2m Homework Equations <H> =E, H = Hamiltonian. p=...

Homework Statement Calculate the average potential and kinetic energies for the electron in the ground state of hydrogen. Homework EquationsThe Attempt at a Solution I know that KE = E - <U(r)>. I know that E = (-KZ^2e^2)/(2a0) and I know that U(r) = -KZe^2/r but I can't figure out how to...

Using the single-electron wave function ψ(r) = N*exp( −ζr2 ) with ζ a variational parameter, how can we calculate the best approximation for the ground state energy of the hydrogen atom?

A check my work question... Homework Statement Louis de Broglie tried to explain Bohr’s hydrogen atom electron orbits as being circles of just the right circumference such that an electron of the Bohr energy going around the circle will interfere constructively with itself. This seems to...

Can you please explain the difference between ground state and stationary state? In the stationary state, are the electrons at rest inside the atom?

< Mentor Note -- thread moved to HH from the technical chemistry forum, so no HH Template is shown > I need someone to check my answers and help me with the questions I couldn't answer. What is the max. # of electrons located in the groud state of a) an orbital 2 b) d sublevel 10 c) Be atom...

Homework Statement Assume a particle is in the ground state of an infinite square well of length L. If the walls of the well increase symmetrically such that the length of the well is now 2L WITHOUT disturbing the state of the system, what is the probability that a measurement would yield the...

Homework Statement Homework Equations $$ \psi_{100} = \frac {1}{\sqrt{\pi a^{3}}} e^{-r/a} $$ The Attempt at a Solution a) $$\langle r \rangle = \frac {1}{\pi a^{3}} \int_0^{2 \pi} d \phi \int_{0}^\pi d \theta \int_0^{\infty} r^{3} e^{-2r/a} dr$$ This comes out to be ##\frac {3}{2}a##...

Homework Statement I am working through a time independent perturbation problem and I am calculating the first order correction to the energy, and I am stuck operating the perturbation : v = i b (Exp[i g x]-Exp[-i g x]) on the ground state |0>. Homework Equations <0| v |0> = 1st order...

This question is in regards to the degeneracy of states for an Argon atom with just one missing electron. For hydrogen the problem of finding the partition function depends on finding the the ionized state of hydrogen divided by the non-ionized state... (please see Saha equation ->...

Homework Statement For a hydrogen-like “atom” (e.g., He+ ion), with nuclear charge Ze, it is claimed that the the ground-state wavefunction is spherically symmetric and is given by ψ(r)=Aexp(−αr) , where A and α are constant. (a) Determine the normalization constant A in terms of α. (b)...

When i take a coherent state ##|\alpha>## if ##\alpha -> 0## then the limit is the Fock state for n = 0. so ##|n = 0> = |\alpha = 0>## The problem is that they seem to have different http://www.iqst.ca/quantech/wiggalery.php: Where is the error? Thanks. Edit sorry, in the link the W function is...

Notation: ##J^p## - ##J## the total angular momentum, ##p## the parity = ##+## or ## -. ## Ok so I'm given a diagram of energy levels, all have a ground state of ##0+##, except one which has a ground state of ##1+##. I'm askeed to indentify which set of energy levels belong to which nucleus...

Hi Physics Forums! The ground state electron is the largest negative value, but what does this mean? Does this mean that kinetic energy is a positive value above zero? It seems at the ground state, the electron might also have kinetic energy as it is moving around as well as potential...

Hello All, I am pretty sure that when a nucleus decays via e.c. and goes to the ground state all of the excess energy is released with the emission of the neutrino but was wondering if anyone could confirm/give a reference for this. Thanks!

Dear all, periodic DFT codes (e.g. VASP) effectively simulate an infinite crystal due to the periodic boundary conditions. However, the energy value that one obtaines at the end of a simulation if finite. Frankly, I'm quite confused right now. Is the energy to be understood 'per unit cell'...

Homework Statement Consider a one-dimentional particle in a box with infinite potential walls at x=0 and x=L. Employ the variational method with the trial wave function ΨT(x) = sin(ax+b) and variational parameters a,b>0 to estimate the ground state energy by minimising the expression E_{T}=...

Hi guys! Suppose there's a particle in a box, initially in its ground state. Suppose that one chooses a system of coordinates such that the potential V(x) is 0 from 0 to L. Suppose that one suddenly perturbate the system at a particular time so that V(x) becomes 0 from 0 to 2L. I've calculated...

Hello everyone: I didn't have a complete view of the quantum field theory and cannot understand this question. We now there will always be fluctuation field in the universe which corresponds to the ground state energy 1/2hw of harmonic oscillator. In the free space, we will use box...

Homework Statement At t<0 a particle is in the ground state of the potential V(x)= \frac{1}{2} mw^2x^2 . At t=0 the potential is suddenly displaced by an amount x0 to V(x)= \frac{1}{2} mw^2(x-x_0)^2 . a) What is the probability of the particle being in the ground state; the first excited...

Suppose you have the transition amplitude in the presence of a source <q''t''|q't'>_{f} To extract the ground state, we change the Hamiltonian to H-i\epsilon , because we can write: $$|q't'>=e^{iHt'} |n><n|q> \rightarrow e^{iE_0t'} |0><0|q>=<0|q>e^{iHt'} |0>=<0|q> |0 t'> $$ where only...

From the ground state wave equation the most probable outcome of anyone measurement will be in the center of the atom, at the nucleus. The expectation value is found to be the Bohr radius. So does this mean that if you measure the position of an electron in a hydrogen atom in the ground state...

Homework Statement Hello! I am trying to derive the ground state enegry of a hydrogen atom, and have come to U=\frac{-mk_{0}^{2}Ze^{4}}{n^{2}\hbar^{2}} Problem is, I know there should e another factor of 2 in the denomenator because I get the ground state energy of hydrogen as being 27.145eV...

In a past physics gre question (https://www.physicsforums.com/showthread.php?t=192334), we make use of the idea that the ground state energy of two ions that have spin is when the spins are aligned. However, the ground state of the helium atom is a spin singlet state, which is a linear combo...

Homework Statement The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. \hat H = \hat H_1 + \hat H_2 + \hat H_{1,2} The wave function for parahelium (spin = 0) is \psi(1,2) = \psi_S(r_1, r_2)\dot...

Homework Statement 2N fermions of mass m are confined by the potential U(x)=1/2(k)(x2) (harmonic oscillator) What is the ground state energy of the system? Homework Equations V(x)=1/2m(ω2)(x2) The Attempt at a Solution I know the ground state energy of a simple harmonic...

I was thinking of putting together a visualization of electron orbitals as it transitions from unbounded or weakly bounded state to the ground state. However, it occurred to me that orbitals are symmetric about the proton. At some point the probability distribution must become asymmetric...

Homework Statement The interaction between the spins of the two particles in a hydrogenic atom can be described by the interaction Hamiltonian $$\hat{H_I} = A \hat{S_1} \cdot \hat{S_2}.$$ Compute the splitting of the ground state due to ##\hat{H_I}##. Both particles have spin 1/2. Homework...

My textbook says the ground state energy of the QSHO is given by 1/2*h_bar*w and that this is the minimum energy consistent with the uncertainty principle. However I am having trouble deriving this myself... ΔEΔt ≥ h_bar / 2.. so then ΔE/Δfrequency ≥ h_bar / 2... ΔE*2*pi / w ≥ h_bar / 2 ΔE ≥...

Homework Statement The normalized energy eigenfunction of the ground state of the hydrogen atom is ##u_{100}(\underline{r}) = C \exp (-r/a_o)##, ##a_o## the Bohr radius. For this state calculate 1)##C## 2)The radial distribution function, the probability that the electron is within a...

Just curious: if an electron absorbs a photon of energy, it is in an excited state. The electron may go to a lower energy state (but NOT the ground state). Can a photon (of higher wavelength than absorbed) be emitted still? I don't quite see the importance of the electron having to go to the...

Homework Statement We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the Heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation. Homework Equations Below The...

In my book it is mentioned that for the two 1s electrons the ground state is the singlet while for the two 2p electrons the ground state could be either singlet or triplet. Generally how can you determine whether the ground state is singlet or triplet?