The hydrogen tag has no wiki summary.
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Hydrogen radial wave function infinity at r=0
When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts:
$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta)$
I understand that the radial part ...
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4answers
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What does ionization of neutral Hydrogen have to do with “transparency”?
Most accounts of the early history of the Universe make some reference to (re)ionization as being the reason that the Universe becomes transparent after a period of opacity caused by the absence of ...
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magnetic moment of proton
I just tried to calculate the magnetic moment of a proton. I took the
proton g-Factor of $g=5.585694$
nuclear magneton of $\mu_k = 5.050783 * 10^{−27}$ J/T
proton spin of $I=1/2$
At first I ...
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2answers
176 views
Technical detail in the solution of the hydrogen atom
I'm trying to do an exercise in which you solve the Schrödinger equation for the hydrogen atom. Through the exercise, I've already shown that the wavefunction is:
$$ \psi_{n\ell m}(r,\theta,\varphi) ...
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1answer
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Scattering states of Hydrogen atom in non-relativistic perturbation theory
In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states
$$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
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1answer
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Stark Effect on the 1st excited state of Hydrogen
I know the ground state of hydrogen is unaffected by the Stark effect to first order. And I also know that the 1st excited state is split from 4 degenerate states to 2 distinct, and 1 degenerate state ...
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3answers
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Bessel vs. modified Bessel in radial equation of hydrogen
I am trying to understand the difference between Bessel functions and modified Bessel functions (simply googling is yielding complicated, non-intuitive answers). I was under the impression that one ...
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4answers
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Could hydrogen liberated from water provide lifting energy which exceeds the energy it took to liberate it from water
I was thinking about Hydrogen balloons and that large ones which are used for weather balloons which sometimes go up to 100,000 ft (approx 30km). Then I was wondering, how much potential energy has ...
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Jupiter Core is Solid Hydrogen
I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an ...
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Why is the binding energy per nucleon not zero for hydrogen atom?
The lone proton has not to be worked on against any electrostatic force. So where does the energy come from? What is mass defect for a hydrogen nucleus?
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4answers
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why ammonia is not a competitive energy carrier?
reading this article about Germany planning to store renewable energy as hydrogen gas, i'm left wondering why they deem so great this plan, compared with other alternatives like ammonia as a energy ...
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1answer
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can hydrogen stay frozen in vacuum?
I've look into the hydrogen state diagram, and it seems that it can be frozen under pressure.
Question: Does this mean that hydrogen cannot be kept frozen in a vacuum chamber?
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How can one describe electron motion around hydrogen atom?
I remember from introductory Quantum Mechanics, that hydrogen atom is one of those systems that we can solve without too much ( embarrassing ) approximations.
After a number of postulates, QM ...
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1answer
42 views
Hydrogen wave function in momentum space
We can seperate the wave function of an hydrogen atom in a radial and an angle part:
$$
\phi_{n,l,m} (\mathbf{r}) = R_{n,l,m}(r) Y_{l,m}(\vartheta,\varphi) \, ,
$$
where $Y_{l,m}$ are the spherical ...
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1answer
180 views
Electric dipole transitions/expectation value of position
Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have
$$
\int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0
$$
for the position vector $\vec{r}$. (This is for ...
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1answer
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How does the internuclear repulsion vary in Hydrogenic atom collision?
Hydrogen fusion requires two hydrogen nuclei to get close enough (typically a few fm) to fuse. Much of the problem of creating a fusion reactor is overcoming the Coulomb repulsion between a pair of ...
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2answers
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Why the hydrogen radial wave function is real?
Why the hydrogen radial wave function is real?
Is it a coincidence?
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2answers
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What's the difference between two Hydrogen atoms?
If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location ...
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1answer
269 views
Theoretical treatment of Hydrogen bond?
I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from ...
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1answer
426 views
Wave function of hydrogen atom including spin of nucleus
How do I write the wave function of hydrogen atom taking into consideration of nucleus spin? For example consider $2S_{\frac{1}{2}}$ state with nucleus spin $I$, then wave function ...
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1answer
331 views
Metallic Hydrogen and Gaseous Planets
Jupiter has about twice the density of Saturn (1.33 versus 0.69 g/cm^3) because it apparently has a higher mass percentage of rocky core and of metallic hydrogen in its interior. Available density ...
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Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?
This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist ...
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3answers
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Water, can it break through temperature?
If water is heaten up to ridicilously high temperatures, is it possible for the atoms in the molecules to lose their bonds?
And if it is possible, isn't this some kind of chain-reaction?
Like you ...
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2answers
273 views
Hydrogen 2P Probability Density Question
I'd like to calculate the probability density for Hydrogen in the $|2,1,1\rangle$ and $|2,1,-1\rangle$ states. There is an $\exp(\pm i\phi)$ term attached to the wave function for these states. It ...
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1answer
66 views
Spectrum measurement
How can be spectrum of hydrogen measured (Lyman series, Balmer series, Paschen series and so on)? I mean schema of measurement circuit and the measuring technique (including all the steps needed). Is ...
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2answers
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Hydrogen atom in quantum mechanics
I have problems following the calculations in Griffiths' Introduction to Quantum Mechanics (Chapter 4.2.1):
If you apply the Schrödinger equation to the Coulomb potential you get the following ...
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1answer
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Finding the wavelength of an electron in its ground state?
To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following?
Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$
Solve for $p$
Use ...
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1answer
64 views
Ground state energy of hydrogen molecule ion
In this paper, it is mentioned:
Furthermore, since the
energy of $H_2^+$in the ground state must be lower than that of an
H atom in the ground state,the negative (attractive) forces in the
...
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2answers
468 views
Wave function of Hydrogen Atom
Wavefunction of a Hydrogen atom is expressed in eigenfunctions as:
$$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$
Is ...
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3answers
266 views
Expectation values of $(x,y,z)$ in the $|n\ell m\rangle$ state of hydrogen?
Expectation values of $(x,y,z)$ in the $| n\ell m\rangle$ state of hydrogen?
Does anyone know of a quick way of finding this (if there is even one)? Can I somehow use the relation that:
$$\langle ...
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1answer
77 views
Hydrogen Hyperfine Structure: General Expression
I was looking at the hyperfine structure for the hydrogen atom. I checked pretty much every textbook I knew but none of them gave me the general expression for the energy correction due to the ...
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0answers
63 views
Geometric quantization of a hydrogen atom
I want to know how to quantize a hydrogen atom as an example of geometric quantization. Apparently there is a derivation in the book "Geometric Quantization in Action: Applications of Harmonic ...
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How to liquefy Hydrogen?
I have got a science project and my teacher has recommended me to do "Liquefying Hydrogen". I have been continuously thinking about that but I have not come to a solution. Can anyone please tell me ...
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Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]
I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks!
Consider the Hydrogen Atom Hamiltonian:
$$
H = (\mathbf p^2/2 ...
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3answers
202 views
Is energy conserved in decay of hydrogen atom in superposed state?
This looks like a paradox.
Let's say we have an hydrogen atom. Superposition of states could be possible for electrons. But if an electron is in a superposition, I guess it could decay into a lower ...
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1answer
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Difference between atom and elementary particle questioned
Hydrogen ion doesn't have one electron which clearly mean that it has only one proton..So hydrogen ion is only a proton. Am I right, please make it clear. If hydrogen ion and proton are same that how ...
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377 views
Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]
I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically:
...
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1answer
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Can atmospheric hydrogen be collected for use?
Just what the title states.
Free hydrogen accumulates in the exosphere. At high altitudes there are large volumes of open space between molecules - which would be a hindrance to collection.
Would ...
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How strong are Hydrogen bombs? [closed]
Yes I searched for answers on Google and here if you must ask.
(Story begins)
My question is about Hydrogen Bomb a.k.a. H-Bomb. On history class teacher told us that two atomic bombs where thrown on ...
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amount of hydrogen necessary to lift one pound, 200 pounds [closed]
How many cubic feet of Hydrogen does it take to lift a 1 pound object, and is the relationship between cubic feet and pounds linear, in other words would it take 200x that amount to lift 200lbs?
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Evaluating Transition probability between different states of Hydrogen atom
I am trying to evaluate the inner product $<2S_{\frac{1}{2}},F',F'_{3}|\delta^{3}(x)\sigma_{i}P_{i}|2P_{\frac{1}{2}},F,F_{3}>$ It's written in the form $<nl_{j},F,F_{3}|$ Where ...
