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 ...

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2
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0answers
36 views

Energy Spectrum and Gauge Transformations

There is a question in SE about the fact that the Hamiltonian isn't invariant under the EM gauge transformations. I wanted to ask about its consequences here. I know that in general, the Hamiltonian ...
0
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1answer
23 views

Corrections to the Bohr energies of Hydrogen [on hold]

Among fine structure, Hyperfine splitting and Lamb shift, why Hyperfine splitting is the smallest while Fine structure is the largest?
-1
votes
0answers
20 views

What is the position of hydrogen in the periodic table? [migrated]

Hydrogen is not in the first group as it was before and it is now placed above the periodic table? So why is it still categorized as a metal in some books?
0
votes
0answers
34 views

Expectation value of radius of hydrogen atom [closed]

As an excercise, I have to do the following: The hamiltonian of the hydrogen atom is given. Try to find the radial part $f(r)$ of the wavefunctions by assuming it to be a power series and show that ...
1
vote
1answer
46 views

Most probable radius of hydrogen in its ground state [closed]

I'm having trouble understanding how we do this. I know we must find the probability density function and then we can optimise it to find the most probable radius. I thought we would just take the ...
0
votes
0answers
17 views

Darwin term affecting hydrogen s-states

The Darwin term, a correction to the non-relativistic hydrogen Hamiltonian due to the zitterbewegung of the electron, is given by $$H_{Darwin}=\frac{e^2\hbar^2}{8m^2c^2\epsilon_{0}}\delta^3(\...
-3
votes
1answer
99 views

How is hydrogen fine structure currently accounted for? [closed]

At a usually reliable site, Hyperphysics, the fine structure of Hydrogen is accounted for by the interaction between the B-field generated by the orbit of the electron, $0.4\:\mathrm{T}$ at $1s$ and $...
3
votes
0answers
44 views

Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
6
votes
7answers
2k views

Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
0
votes
1answer
24 views

Why can the 2p0 to 1s transition in hydrogen with dipole interaction not be solved without splitting into x,y,z polarisation?

The $2p_0$ and $1s$ wavefunctions for hydrogen; $ \psi_{2p_0} = \dfrac{1}{4\sqrt{2\pi}} \left(\dfrac{Z}{a_b}\right)^{\frac{3}{2}} \dfrac{Z r}{a_b} e^{\frac{-Zr}{2a_b}} \cos(\theta) $ $ \psi_{1s} = ...
0
votes
0answers
6 views

Why are these H cross sections given as a function of energy per amu?

The Atomic and Plasma-Material Interaction Data for Fusion Vol. 4 (1993) by the IAEA lists empirical fits for ionization and excitation of hydrogen by collisions with $\mathrm{H}^{+}$. The fits are ...
3
votes
1answer
32 views

Higher order corrections to hydrogen and their consquence

I was wondering if there have to be higher order corrections for the quantum mechanical description of the Hydrogen atom. I'm aware that there are relativistic corrections and also QED corrections. ...
1
vote
2answers
54 views

What don't electrolysis produce a vast amount of hydrogen?

In my research and by asking questions on sites like this. I have learned that why using electricity in water can make hydrogen using the process electrolysis, why isn't it the most effective way? To ...
3
votes
1answer
42 views

Spectroscopic properties of hydrogen: H vs. H2

One of the basic experiments everybody learns about when it comes to physics is the spectroscopy of hydrogen gas. The typical set-up has a charge discharge lamp containing the hydrogen. The resulting ...
4
votes
3answers
124 views

Why does a “typical” hydrogen atom have no neutron?

There are quite a few sources (mostly high-school physics textbooks) that I've read which don't give the disclaimer that the hydrogen atom they are using in a diagram is an isotope (as in having ...
3
votes
1answer
44 views

Hydrogen Ground State Energy

Using the non-relativistic Schrodinger equation, the energy levels for hydrogen are found to be $E_{n} = -\frac{1}{2n^2}mc^2\alpha^2$. Using the relativistic Dirac equation, the energy levels for ...
10
votes
1answer
162 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ \left(-\frac{\hbar^2}{2\...
1
vote
1answer
36 views

Energy of photon after emission

Exercise: A hydrogen atom is at its first excited state. When it de-excites it emits a photon. What is the energy of the photon and the kinetic energy of the atom? Question: Is it correct to ...
2
votes
2answers
110 views

What is the difference between metallic hydrogen and plasma of hydrogen?

As far as I know, metallic hydrogen and plasma seems share some common properties, eg:conduct electricity, nuclei share electrons, high temperatures... So my question is, is metallic hydrogen in fact ...
3
votes
1answer
71 views

Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
0
votes
0answers
12 views

Hydrogen pressure in fuel cell

It takes energy to compress hydrogen tot 350 or 700 bar. Can some of this compression energy be recovered in the fuel cell? Higher pressure of Hydrogen leads to and increased open cell voltage n the ...
0
votes
0answers
32 views

Which Hydrogen Emission Lines Appear First?

When a blackbody is heated, it radiates photons. At low temperatures, there isn't much radiation at high-energy end of the spectrum but as the temperature raises, high-energy radiation becomes ...
0
votes
0answers
39 views

Fuel cell HHV vs LHV

I am calculating the maximum efficiency for a fuel cell, based on both HHV and LHV. For hydrogen and oxygen in a PEMFC I calculated these at STP as 82.9% (based on HHV) and 94.5% (based on LHV). I do ...
4
votes
1answer
74 views

How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
0
votes
2answers
42 views

Why does parahydrogen have a lower energy than orthohydrogen?

I found this on the wikipedia page on spin isomers of hydrogen: Parahydrogen is in a lower energy state than is orthohydrogen. It seem almost like it is obvious but I am having trouble reasoning ...
0
votes
3answers
147 views

Why can't space become fuel for spaceships? [closed]

I read somewhere that space is constitued mostly of hydrogen. So why can't space and its constituants (not only hydrogen) serve as fuel for future spaceships? The dreamer I am simply imagine a ...
3
votes
1answer
67 views

In the LHC, how is the proton separated from the electron in the hydrogen? [duplicate]

I know that we use protons in the LHC. So my question is, how is the proton separated from the electron in the hydrogen?
0
votes
1answer
22 views

Rydberg and electrical energy

I am a high school student. This year I learned the Rydberg constant and its use of finding energy of an electron in chemistry, besides in physics I learned to calculate the energies of two loaded ...
-2
votes
2answers
85 views

Could I create a banana? [closed]

As I understand it, until such time as stars were formed and heavier elements could be created, there was just hydrogen and helium, plus trace amounts of lithium an beryllium. Question: if everything ...
4
votes
1answer
125 views

$SO(4,2)$ symmetry of the hydrogen atom

The hydrogen atom with Hamiltonian obviously has $SO(3)$ symmetry since it just depends on the radius. $$ H = \frac{\mathbf{p}^2}{2m} - \frac{k}{r}$$ This is generated by angular momentum $\mathbf{L}...
2
votes
1answer
72 views

Will hydrogen die out? [duplicate]

Stars create heavy elements up to iron during their lifetimes, and heavier elements beyond iron during supernova events. Are there any processes which create new hydrogen? If not, will all (or most) ...
1
vote
1answer
77 views

Do plasmas have their own magnetic fields?

Do Plasma generate a magnetic field of their own ? Can they cause electromagnetic induction?? For example if a hydrogen plasma is ionized and its electrons removed.. And the protons accelerated ...
1
vote
0answers
58 views

Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l ...
0
votes
1answer
78 views

Z coordinate expectation value of the Hydrogen atom

I want to find $z-coordinate$ expectation value $\textbf{<z>}$ of the Hydrogen atom wave function $\psi_{1,0,0} = (\pi a^3_0)^{-1/2}e^{-r/a_0}$ in its ground state. I read in some text that $&...
0
votes
0answers
9 views

Why does concentrated parahydrogen in hydrogenation reaction exhibit hyperpolarized signals in proton NMR spectra?

In wikipedia it says "When an excess of parahydrogen is used during hydrogenation reactions (instead of the normal mixture of orthohydrogen to parahydrogen of 3:1), the resultant product exhibits ...
1
vote
1answer
40 views

Water + RF + Spark = Continuous Fire

Can anyone explain the physics of what is happening in the following video? https://youtu.be/p8xYUDiSGDk?t=37 Is this process Radiolysis? At what radio frequency & power level is h20 ...
0
votes
0answers
15 views

How is the Lyman alpha forest and Gunn-Peterson trough evidence for Reionization? [duplicate]

I'm trying to understand how the Lyman alpha forest and Gunn-Peterson trough are evidence for Reionization. From what I've read, the Lyman alpha forest tells us how much neutral hydrogen is in the ...
1
vote
1answer
95 views

Deriving the Bohr radius of a hydrogen atom using Schrödinger's equation

I'm trying to follow the book for the introduction to quantum mechanics by Griffiths. I'm following the part where he is solving Schrödinger's equation for the hydrogen atom. There, he found the Bohr ...
-1
votes
3answers
88 views

Complex conjugate of hydrogen ground state wave function [closed]

For hydrogen atom ground state we know . I want to know the complex conjugate of .
2
votes
2answers
127 views

Temperature of fusion in the Sun vs. fusion in controlled experiments on Earth

I recently learned that hydrogen fusion (i.e., hydrogen to helium) experiments on Earth have been successful at temperatures in excess of 100,000,000 degrees Celsius. However, I also learned that ...
0
votes
1answer
73 views

How does speed of gas molecules change with pressure? [closed]

A thought experiment. I have a box of fixed dimensions, inside this box I have molecules of $H_2$ at constant temperature. I'll be gradually increasing pressure inside the box and the temperature ...
0
votes
1answer
62 views

Does the proton wobble due to the electron's orbit in a Hydrogen atom?

In a hydrogen atom the nucleus only has one proton and no neutrons so the electron to nucleus radio is higher for hydrogen than that for any other atom. Does the orbiting electron induce a wobble on ...
2
votes
0answers
43 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = \left\{\...
1
vote
1answer
51 views

The point of charge neutrality in the Hydrogen Atom

If we treat the Hydrogen Atom like the Bohr model then we have a proton in the center with an electron orbiting at some radius (the Bohr radius). In this picture you can imagine the electric field ...
3
votes
2answers
152 views

In the hydrogen atom, why is the electron orbital spherical rather than flat like a 2D orbit plane?

In a hydrogen atom an electron is orbiting around a proton, similarly to a moon around a planet. The orbit of a moon around a planet is flat (2D) whereas the orbit of an electron around a proton is ...
3
votes
2answers
128 views

Why is the blue line in the Balmer series sometimes not visible?

So I've conducted an experiment to find the four visible hydrogen emission spectrum lines in the Balmer series in a laboratory. I don't have any background in quantum physics. When I looked through ...
0
votes
1answer
85 views

Confused on how to interpret the energy eigenfunction of Hydrogen

So here is an image of the third lowest energy eigenfunction of an electron in a hydrogen atom: Image from http://imgur.com/Lu4MocL I understand well the eigenfunctions given by Schrodinger's ...
1
vote
1answer
42 views

Hyperfine lifetime calculation: what is the spin eigenfunctions?

I'm trying to calculate the lifetime of the 21 cm line in hydrogen and have the following expression: $\frac{1}{\tau} = \frac{4\alpha}{3}\omega_{if}^3|\langle a_f|\vec{x}|a_i\rangle|^2$. The ...
0
votes
3answers
93 views

Quick way to compute $\langle n^{'}l^{'}m^{'}|r^k|nlm \rangle$, $k \in I$; $|nlm\rangle$ is $H$ atom eigenfunction [closed]

I want to compute quickly (using maybe some scaling arguments) $\langle n^{'}l^{'}m^{'}|r^k|nlm\rangle$, where $k \in I$. $|nlm \rangle$ is the eigenfunction of the Hydrogen atom ($H$). Example: ...
1
vote
1answer
59 views

Fusing Hydrogen with lightning

I've been reading about fusion recently (Specifically Deuterium fusion) and a friend of mine asked me if it was possible to fuse two Deuterium atoms with a lightning strike? Now this question has a ...