Could refer to (1) A hydrogen molecule; two hydrogen atoms bonded together or (2) A hydrogen atom; One electron electromagnetically interacting with a nucleus made of a single proton. Hydrogen atoms are the simplest atoms, and they are the only atoms for which we can exactly solve the Schrodinger ...

learn more… | top users | synonyms

14
votes
3answers
2k views

How long will the Universe's hydrogen reserves last for?

I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions. Here ...
13
votes
1answer
1k views

How would one detect antihydrogen in the universe?

Since the spectra of hydrogen and antihydrogen are the same, how do astronomers know which one they're detecting? Is, perhaps, the Lamb shift in antihydrogen different?
12
votes
5answers
1k views

How does the hydrogen atom know which frequencies it can emit photons at?

At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the ...
7
votes
3answers
1k views

What is the unit of time on the Voyager Golden Record?

What is the unit of time on the Voyager Golden Record? Apparently, it has something to do with "a fundamental transition of the hydrogen atom". A high-level description was provided by NASA, as ...
7
votes
2answers
539 views

How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
7
votes
4answers
685 views

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 ...
7
votes
3answers
486 views

Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
7
votes
2answers
239 views

How does one calculate where the “surface” of a gas-giant would be?

Okay, so Jupiter, Saturn, et. al are gas giants. I understand that they have large gassy atmospheres, which, due to the pressure would eventually become more and more dense as one approaches the ...
6
votes
1answer
73 views

How did Lyman discover his series?

How did Lyman discover his series in hydrogen atom? How did he know that the final energy level is the first level and not the second or the third or etc.? Or how did the other scientists know which ...
5
votes
3answers
726 views

Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
5
votes
2answers
1k views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum.But, I was wondering why he quantised angular momentum and any other quantity?
5
votes
1answer
736 views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
5
votes
1answer
643 views

Reduced mass in quantum physics (Hydrogen Atom)

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
5
votes
2answers
440 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) ...
5
votes
1answer
443 views

How can we describe the electrons of multi-electron atoms (i.e. not Hydrogen) when equations/analytic solutions only exist for Hydrogen?

I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the single electron in the ...
5
votes
2answers
190 views

Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
5
votes
0answers
95 views

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 ...
4
votes
5answers
1k views

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 ...
4
votes
4answers
193 views

How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
4
votes
1answer
288 views

Fusion: Why deuterium and tritium?

I would like to know why scientists try to use deuterium and tritium for fusion and not just the ordinary isotope of Hydrogen ${}^1H$?
4
votes
4answers
3k views

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 ...
4
votes
3answers
107 views

Hydrogen cloud at the universe's beginning?

What prevented all of the hydrogen at the universe's start from coalescing into one gigantic star?
4
votes
2answers
1k views

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 ...
4
votes
1answer
344 views

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' ...
4
votes
2answers
355 views

Neil deGrasse Tyson says that electrons “teleport” between energy levels?

This page: https://blog.afach.de/?p=62 Discusses the error Neil deGrasse Tyson made when talking about electronic transitions (video included there). Tyson clearly said in his Cosmos series that ...
4
votes
1answer
1k views

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 ...
4
votes
1answer
462 views

What are independent parameters in Hellmann–Feynman theorem?

A typical example in textbooks about the application of Hellmann–Feynman theorem is calculating $\left\langle\frac{1}{r^2}\right\rangle$ in hydrogen-like atoms. Wikipedia has a nice demonstration of ...
4
votes
1answer
85 views

Does first quantization perturbation theory imply a large scale web of electron entanglement?

My question may seem quite esoteric given the title, but I think it's relatively straightforward when explained properly. Imagine a relatively simple situation of 2 hydrogen atoms (numbered 1 and 2), ...
4
votes
2answers
946 views

Where does the Pauli Repulsive Force come from that counteracts the attraction between atoms and ions? [duplicate]

I'm learning about such things as ionic and covalent bonds, and the reason given for the ionic bonds is electrostatic attraction. However, if that were true, then the two ions would accelerate toward ...
4
votes
2answers
858 views

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 ...
3
votes
3answers
533 views

Why do we use the Coulomb potential for the hydrogen atom?

When solving the Schrodinger equation for the hydrogen atom, the Coulomb potential $V = \frac{e^2}{4 \pi \epsilon_0 r}$ is used. The Coulomb potential comes from classical electrodynamics, so why ...
3
votes
3answers
357 views

Why are hydrogen energy levels degenerate in $\ell$ and $m$?

Is there a good physical picture of why the energy levels in a hydrogen atom are independent of the angular momentum quantum number $\ell$ and $m$?
3
votes
3answers
440 views

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 ...
3
votes
4answers
656 views

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 ...
3
votes
1answer
128 views

Calibrating the relative intensity of a spectrometer with a blackbody source?

I am trying to compare the relative brightness of H-Beta and H-Alpha lines using a CCD spectrometer. In order to correct for the different grating efficiency at the two different wavelengths. I took ...
3
votes
1answer
985 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 ...
3
votes
1answer
65 views

State with non-zero angular momentum - cannot be described by spherical harmonic?

For a state with non-zero angular momentum, why is it that it cannot be described by the spherically symmetric spherical harmonic?
3
votes
2answers
424 views

What is the expected distance of the electron from the nucleus in the hydrogen atom?

Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$). I understand that it ...
3
votes
2answers
1k views

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?
3
votes
2answers
196 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
2
votes
4answers
1k views

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 ...
2
votes
1answer
221 views

Orbital of Hydrogen molecule

does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an ...
2
votes
2answers
304 views

Why the hydrogen radial wave function is real?

Why the hydrogen radial wave function is real? Is it a coincidence?
2
votes
1answer
153 views

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?
2
votes
2answers
859 views

Calculating the most probable radius for an electron of a hydrogen atom in the ground state

This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state. It states that : The radial probability density for the hydrogen ...
2
votes
2answers
285 views

Spin orbit coupling and fine structure of the Hydrogen atom

At university we have just derived the expression for the energy split due to spin-orbit coupling in the Hydrogen atom, i.e. what is known as the FINE structure of Hydrogen. To do this, we ...
2
votes
1answer
191 views

Volume charge density of H-atom

I have a problem where I am supposed to calculate the volume charge density of a neutral hydrogen atom. The potential is given to be $$ \Phi = k \frac{e^{-ar}}{r} \left(1 + \frac{ar}{2}\right) $$ Now ...
2
votes
1answer
268 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 ...
2
votes
2answers
339 views

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 ...
2
votes
2answers
506 views

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 ...