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from the partition function - am trying to show that ##\langle \mu \rangle = \beta^{-1} (\partial \log Z / \partial B)## where ##Z## is the canonical partition function for one atom, i.e. ##Z = \sum_{m=-j}^{j} \mathrm{exp}(\mu_0 \beta B m)##, and ##\mu = \mu_0 m##. The average...
This is actually a two-part question:
1) According to the Copenhagen Interpretation, atoms have energy bands but there's no explanation of how these bands are derived, or why they only form for protons/antiprotons. Any thoughts?
2) The Copenhagen Interpretation mentions that when an atom's...
Consider electrons in atom, and let's mostly ignore interactions between the electrons for now. What I mean by that is that the lowest energy level is the doubly degenerate 1s, then the doubly degenerate 2s, then the 6-fold degenerate 2p, etc.
Textbooks like Griffiths use term symbols...
I can look at it as if a vibrational motion of the atoms was a simle harmonic motion. So I can consider one of the two atoms to be at rest and the second one to vibrate. Its deviation can be written as ##x(t)=r(t)-r_0##.
When I know that the hydrogen molecule stops exiting when the range of...
I'm going to be a bit sketchy here, at least to start with. If you want me to show you exactly where I am I might post a pdf, if that's okay. (Only because it will simplify coding several pages of LaTeX.)
Briefly, what I'm trying to do is take this system of equations:
##F^{ \prime } +...
The proton and electron are described by separate wavefunctions.
When they come together in the hydrogen atom are they quantum entangled and have a joint wavefunction.
Given the definition of whole numbers as integers, https://www.google.com/search?q=what+is+a+whole+number&rlz=1C1VDKB_en-GB&oq=what+is+a+whole+number&aqs=chrome..69i57j0i512l9.11619j0j15&sourceid=chrome&ie=UTF-8
Is it known why atom vibrations are only at whole numbers ( ref plank’s constant)...
Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of...
Hello guys, I don't know if this is the right place to ask, so please be kind :/
I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%.
When I asked about the remaining...
my premises:
— one can arrive at the Klein-Gordon equation by applying quantum mechanical operators to the special relativity dynamics equation E^2 = (mc^2)^2 + (pc)^2.
— Schrodinger arrived at this equation, but rejected it because it didn't correctly explain the behavior of an electron in a...
The schrodinger equation for helium is
(−ℏ^2/2me(∇21+∇22)+V(r1)+V(r2)+V(r12))ψ=Eψ
V(r12)=1/(r12-r1) which makes the equation inseparable. Can other methods be used to solve it.
The lowest price for a microscope that can...
What is the cheapest (no not a cheap one but the cheapest) microscope from which atoms can be seen in? I don't need a big zoom into an atom. If possible I would just a zoom enough to see atoms as tiny spheres no structure. Example bellow (this one...
Hi, I have an interview for masters degree program in 2 weeks and they asked to study two subjects thoroughly, first being Hydrogen atom and second being Kepler's laws. anyone recommends one book about each subject with advanced level questions that would help me understand the subjects to a...
Hello! Assume I create an atom by some non-state-selective method (e.g. laser ablation, or hitting a proton on a target) and let's say that the atom is in a ##J=1## state. In the absence of magnetic fields, the ##m_J = 0, \pm 1## levels are degenerate. If I am to define arbitrary a z-axis (say...
I have a question about a sentence in the book Introduction to Thermal Physics (Daniel v. Schroeder).
So in chapter 6, Schroeder talks about an atom isolated. This means its energy is fixed.
The atom is in some state. The energy states of the atom have degenerated. All microstates with that...
I have a problem in calculate a matrix element in a problem with hydrogen atom.
I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element...
I am a little lost on how to approach this problem.
What I know is the following:
The r vector is in terms of x y and z hat.
I know my two l=0 states can be the 1s and 2s normalized wave function for Hydrogen.
Should I be integrating over dxdydz?
Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion?
My intuition is that, whether considered in a classical sense or quantum sense, the speed of a given electron in its motion within an atom will be constant and...
If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...
Particles can be made to be in superposition of their states. Concerning Schrödingers cat, if the cat is in superposition of being dead and alive, does that mean that the atom that drives the narcotic is in superposition of having decayed and not having decayed? And does that mean that any...
Are there any results on the structure of the helium atom eigenfunctions? By this I'm referring to the non-perturbative structure of the eigenfunctions, AKA what are the quantum numbers that one would use to label the eigenfunctions?
I have a question about what happen when an electron in the Bohr model of atom, gains energy because for example is "hitting" by a photon.
Electron have an energy, and it is the sum of potential and kinetic.
When they gain energy, they gain potential energy so they go further away from nucleus...
There is an optimum energy which gives the greatest probability of ionisation of a particular element.
This is said to align with the wavelength of the electron being close to resonances in the atom.
Looking at this in a different way as particles, would it be correct to say that the optimum...
Which one is closer to reality, is it this picture https://en.wikipedia.org/wiki/Hydrogen#/media/File:Hydrogen_atom.svg or this https://www.naturphilosophie.co.uk/heart-hydrogen-atom/? The reason why I asked the question is according to the picture of hydrogen atom at Wikipedia, which is the...
We know heat is the motion of molecules of a gas for example. As temperature increases this motion increases and the gas expands. We know this gas would be hot if we touch it. So I want to ask how does the fast motion of molecules somehow translates to the heat that we feel. Why does it feel...
If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
Hello! I went over a calculation of the hydrogen wavefunction using Dirac equation (this one) and I am a bit confused by the angular part. The final result for the wavefunction based on that derivation is this:
$$
\begin{pmatrix}
if(r) Y_{j l_A}^{m_j} \\
-g(r)...
The information I have are the following:
##p^\mu=(E, p, 0, 0)##
##p'^\mu=(E', p'\cos\beta, -p'\sin\beta,0)##
##k^\mu=\tilde{E}(1, \cos\alpha, \sin\alpha, 0)##
Where:
##E=\sqrt{M^2+p^2}##
##E'=\sqrt{m^2+p'^2}##
Using the conservation of the four-momentum
##p^\mu=p'^\mu+k^\mu##...
Hello everyone! I have two questions which had bothered me for quite some time. I am sorry if they are rather trivial.
The first is about the general solution of the hydrogen atom schrödinger-equation: We learned in our quantum mechanics class that the general solution of every quantum system...
I read this from Nasa's website:
"Within the first second after the Big Bang, the temperature had fallen considerably, but was still very hot - about 100 billion Kelvin (1011 K). At this temperature, protons, electrons and neutrons had formed, but they moved with too much energy to form atoms...
So let's say we have a large neutral atom, e.g. gold with 79 electrons around it. Let's say we replace its outermost electron with a muon. Muons orbit closer to the nucleus than electrons, much closer. Will the outermost muon be closer into the nucleus than even its innermost ground-state...
I think that when an atom of polonium (Po-216) is moving slowly enough that it can be considered to be at rest. The Po-216 undergoes alpha decay and becomes lead ( Ph-212 ), via the reaction 깝 Po → Pb + ta. After the decay. the lead atom is moving to the left with speed v. and the alpha particle...
Textbooks always give an explanation for why electrons move between energy levels in atoms with an explanation something like this:
'An electron can jump to a higher energy level if it absorb's energy which exactly matches the difference between final and initial energy level'.
My question...
If an atom were made to release a Photon, then a number of the components of the atoms nucleus were theoretically extremely quickly removed. would the previously emitted photon change wave length?
Hello! Assume we have a 2 level system, with the ground state defined as the zero energy level and the excited state having an energy of ##\omega_0##. If we apply an oscillating electric field (assume dipole approximation and rotating wave approximation) of frequency ##\omega##, we have a time...
Is there a general rule for a crystal structure how many bonds each atom in the crystal lattice will make ?For example Si has a face centered cubic structure so it makes 4 bonds regardless of the fact Si has 4 valence electrons?
On the first attached page ##\mu_z## is associated with orbital angular momentum (Eq. 41.34). On the following pages (Eq. 41.38) it is associated with spin angular momentum? Are these both part of the same thing? I tried to read further but the book does not address this. In example 41.6 it...
Hi, first-time poster here
I'm a student at HS-level in DK, who has decided to write my annual large scale assignment on Schrödinger's equation. My teacher has only given us a brief introduction to the equation and has tasked us to solve it numerically with Euler's method for the hydrogen atom...
The equation $$\frac{\hbar^2}{2m}\frac{d^2u}{dr^2}-\frac{Ze^2}{r}u=Eu$$ gives the schrodinger equation for the spherically symmetric functions ##u=r\psi## for a hydrogen-like atom.
In this equation, substitute an assumed solution of the form ##u(r)=(Ar+Br^2)e^{-br}## and hence find the values...
In Sheldon Glashow's critical review of "What is Real? The Unfinished Quest for the Meaning of Quantum Physics" by Adam Becker, there is one paragraph I don't understand. In Glashow's thought experiment of a single radioactive atom in a box:
My thought experiment is like Schrödinger’s, but...
Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function:
$$
F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k
$$
that, for ##n=l+1## becomes
$$
F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n
$$
To find ##a_n## I...
When we say energy levels of the hydrogen atom. Are that energies of the atom or of an electron in the atom? Also corresponding states?
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html
Why energies are negative?
E_n \propto \frac{-1}{n^2}
Can someone explain me conceptually how one can use trapped ions to make atomic clocks? My basic understanding of trapped ions is, we can think of an ionized atom which is controlled by electric and magnetic fields. But i am wondering how can one build an atomic clock using trapped ions.
We usually think about atomic orbital as wave(function), but it was created from e.g. electron and proton approaching ~10^-10m (or much more for Rydberg atoms), and electron has associated electric field.
This wavefunction also describes probability distribution for finding electron (confirmed...