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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31 views

Show that the minimum energy value for a given $l$ increases as $l$ increases

"Consider a particle in a central field and assume that the system has a discrete spectrum. Each orbital quantum number $l$ has a minimum energy value. Show that this minimum value increases as $l$ ...
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2answers
63 views

Using slope=0 technique to find most likely spherical shell

In this PDF http://riedo.gatech.edu/Teaching/Modern_Physics/hw/HW3_2010_MP_SOL.pdf problem#1, the instructor solves the question of which spherical shell (what radius $r$) has the greatest ...
0
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1answer
46 views

Why is there no $1S_{-1/2} $ state of the hydrogen atom?

Heyho, i found this term scheme for the hydrogen atom: https://upload.wikimedia.org/wikipedia/commons/9/94/Wasserstoff_Aufspaltung.svg I was wondering why there is only a $1S_\frac{1}{2}$ state and ...
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2answers
57 views

What causes the death of the Sun?

In a previous question I learned that in each second only a miniscule portion of the total hydrogen in the Sun is converted to helium and that the number is 1/10^18 of its mass converted each second. ...
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2answers
62 views

Where do atoms of H and He go when they rise in the atmosphere? [duplicate]

What happens to atoms/molecules of H and He when we let them freely fly in atmosphere do they get into space? Is there any particular way to enumerate the 'force' that drives them upwards? Does ...
0
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1answer
65 views

Where is the Hydrogen the Sun consumes?

I understand the Sun consumes 600,000,000 tons of Hydrogen each second. Where is this Hydrogen? Is all the Hydrogen the Sun will ever consume inside it or are there vast amounts of Hydrogen in space ...
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2answers
75 views

Changing coordinates in partial derivatives, re: Hydrogen atom

At around 11:35 in this video https://www.youtube.com/watch?v=q99ygFeWGv4 the instructor is using a "standard way of changing coordinates" in partial derivatives relating to the new variables of ...
1
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1answer
74 views

Width of a 1 dimensional box with same ground state energy as hydrogen atom [closed]

I am trying to find the width $L$ of a one-dimensional box for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom. No ...
0
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1answer
66 views

Can't a hydrogen electron have net positive energy?

This page http://www.physicspages.com/2011/06/07/hydrogen-atom-series-solution/ is the 2nd half of a solution to the hydrogen atom Schrödinger equation. They derive that $E = -1/n^2 *$ (bunch of ...
1
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1answer
83 views

Continuous spectrum of hydrogen atom

I wonder if there is a nice treatment of the continuous spectrum of hydrogen atom in the physics literature--showing how the spectrum decomposition looks and how to derive it.
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2answers
61 views

How is hydrogen stored in hydrogen bombs?

Fusion bombs obviously fuse hydrogen atoms, using the pressure from a fission bomb. But how much hydrogen does it contain, and how is it stored? AFAIK hydrogen easily drops its electron and escapes as ...
1
vote
1answer
39 views

Why is hydrogen, nitrogen, carbon and oxygen the most common constituents of interstellar molecules?

Could someone elaborate more on the use of the word "constituent"? Is the question basically asking why these four elements are the most prevalent in interstellar molecules? If so, why are they the ...
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2answers
40 views

Can high speed moving hydrogen atoms drive turbines?

We know that hydrogen is a part of air so if we accelerate hydrogen atoms in a circular vacuum tube as done in a particle accelerator, can the high speed moving atoms of hydrogen drive a turbine if we ...
2
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3answers
599 views

Pure hydrogen star

What is the smallest mass of pure hydrogen that can ignite fusion? That is can population III stars have tiny masses? How would such stars develop? How long would such a star last?
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1answer
40 views

What is supposed to be used as $m$ in $m\lambda = d\sin \theta $

I know that $m$ is the "order number", but I don't understand how this applies to the lab we did. We looked at Hydrogen gas through a diffraction grating (500 lines/cm or something like that) and saw ...
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1answer
28 views

Plot of fusion energy output growth? [closed]

What would a chart of energy output of elements of mass X fused with hydrogen look like? What about X fused with X?
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1answer
29 views

Is the 21cm line of hyperfine structure hydrogen an allowed transition?

The ground state of hydrogen is $^{2}S_{\frac{1}{2}}$ with nuclear spin $I=\frac{1}{2}$. The levels are split by $F=1,F=0$. By the rules of electric dipole transition, $\Delta l = \pm 1$. But in this ...
13
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3answers
1k views

Why is it so hard to separate isotopes?

I was reading on Wikipedia that heavy water in large amounts is toxic to eukaryotic cells because certain physical properties of deuterium are different enough from those of common protium to disrupt ...
1
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2answers
119 views

Electron energy in hydrogen

Is the energy of the electron in a random hydrogen atom in a superposition of all eigenvalues (some value upon measurement) or you will find it most likely in the ground state. I want to clarify my ...
0
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1answer
48 views

What exactly is closed orbit theory and what assumptions go into it?

I am just beginning a research project on the study of closed orbits, specifically as related to hydrogen, and I wanted a little bit more information on what exactly makes something a "closed orbit". ...
1
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0answers
29 views

Find the fraction of atoms in specific quantum state in stellar atmosphere [closed]

Consider gas consisting of hydrogen atoms at temperature about $T \sim 5 \cdot 10^6 \text{ K} \approx 431 \text{ eV}$ and concentration $N \sim 10^{11} \text{ cm}^{-3}$. I need to find the fraction of ...
4
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2answers
275 views

Using the uncertainty principle to estimate the ground state energy of hydrogen

I have been reading through this estimate of the ground state energy of hydrogen and others like it. In this one it says it is using the uncertainty principal but then proceeded to use the following: ...
2
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1answer
110 views

Algebraic solution of Dirac equation for Coulomb potential

The Runge-Lenz operator enables an algebraic solution of Coulomb potential energy levels without a solution of a differential equation. What is the analog for the solution of the Dirac equation in a ...
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3answers
170 views

Meaning of the Angular Momentum in Quantum Mechanics

There was a discussion about the angular momentum in QM in an online course that I am attending now. The discussion and the answers did not satisfy me so I wanted to ask it on Physics SE. In the ...
2
votes
3answers
272 views

Normalization problem with hydrogen wavefunction

Suppose you have a mix of states made up of the Hydrogen $\lvert nlm \rangle$ states where one of the coefficients is unknown. For example: $$ \lvert \psi\rangle=A\lvert 100\rangle + ...
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0answers
37 views

Experiment validating existence of virtual particle

I'm curious about virtual particle whether do they really exists, therefore I dug out an experimental theory called lamb shift by measuring the difference between the two energy levels of a hydrogen ...
1
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1answer
68 views

2s orbital wavefunction has non-zero probability at $r=0$? [duplicate]

The wavefunction for an electron within a hydrogen atom in the $2s$ state has the following wavefunction: ...
0
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2answers
67 views

How does the time evolution of a hydrogen atom work?

If I am given the initial stationary spatial wavefunction of a hydrogen atom, how does it change through time? I'm wondering if it is the same as the time evolution of any old stationary state, that ...
0
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0answers
33 views

Why does the spectrum for deuterium show a weak line at H-alpha?

I was wondering why the spectrum for deuterium shows a weak line at H-alpha, the first line in the hydrogen spectrum.
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2answers
114 views

How do we know $\psi$ depends on $n,l,m$

Regarding the separation of $\psi$ to an angular and radial part, why does each part have a specific dependence of the quantum numbers? How can Schrodinger equation describe a system just from its ...
0
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1answer
42 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
1
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1answer
203 views

Size of positronium

Positronium consists of an electron and a positron. By what factor is a positronium atom bigger than a hydrogen atom? The solution has been explained to me. The characteristic length when solving ...
1
vote
1answer
131 views

Describe proton and electron by one wavefunction

when I was new into quantum mechanics, I thought we can describe helium atom by two wavefunctions - one for every electron. After some time I discovered how wrong I was - first, because electrons are ...
1
vote
1answer
75 views

Can hydrogen atom state be a superposition of 2 pure states with opposite spin?

The task is: We are performing measurements on hydrogen atom, that is in an unknown state $\psi$. $\psi$ is a superposition of $n=1$ and $n=2$ pure states and is orthogonal to ...
0
votes
1answer
29 views

What is “$f$” in deuterium-hydrogen ratio measurements?

On D-H ratio plots, $f$ seems to be used as a reference point, e.g. on the right axis in this plot of D/H ratios around the solar system from a 67/P paper: What exactly is $f$ and how is it ...
0
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0answers
42 views

Is the associated Laguerre polynomial $L_1^1(x)$ equal to $-1$ or $2 - x$?

I've been reading a book by Normand M. Laurendeau, Statistical Thermodynamics: Fundamentals and Applications, about hydrogen orbitals and in it is an equation that explains how to calculate the ...
3
votes
2answers
136 views

How do you determine the “phase” of a hydrogen eigenfunction?

I've been reading the wikipedia article on the atomic orbitals of hydrogen. They have a nice collection of diagrams, such as this one for n,l,m = 3,1,1 This is apparently showing the wavefunction, ...
1
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0answers
103 views

Is hydrogen atom in a box solvable analytically?

Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ...
1
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0answers
103 views

Hydrogen 2p3/2 -> 1s1/2 transition polarisation and angular distribution

Could you please help me. I have to calculate the intensity angular and polarisation distribution in hydrogen electric dipole transition $\text{2p}_{3/2}\rightarrow \text{1s}_{1/2}$. To do this I ...
1
vote
1answer
107 views

Nuclear fusion - Hydrogen isotopes

What is the isotope composition of hydrogen atoms in the sun? Are the ratios of protium:deuterium:tritium similar to those we find on earth? What does the nuclear fusion of hydrogen atoms in the sun ...
3
votes
3answers
828 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 ...
0
votes
1answer
614 views

Difference between a hydrogen ion and a proton

I've run into a bit of a problem on this weeks coursework. A proton and an electron initially at rest combine to form hydrogen. Find the wavelength of the emitted photon? So, as far as I can ...
2
votes
0answers
30 views

What symmetry operation mixes states with different $\ell$ in hydrogen atom? [duplicate]

We can mix states with different $m$ in hydrogen atom by rotating it around some axis (not coinciding with $z$). Thus rotation is the symmetry operation which mixes states with different $m$. As ...
1
vote
2answers
317 views

Centrifugal force in the Hydrogen atom for $L=0$

I have found the following interesting article: http://arxiv.org/abs/0706.0924 The authors examine the radial momentum operator in detail, in particular its time evolution due to the forces acting ...
2
votes
1answer
69 views

Choice of the z-axis in the Schrödinger equation for the hydrogen atom

I am reading about the solution of the Schrödinger equation for the hydrogen atom and have a question about the choice of the z-axis. Most websites say that the z-axis is arbitrarily chosen. If so, ...
4
votes
4answers
275 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 ...
0
votes
2answers
155 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar, \qquad ...
15
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?
3
votes
2answers
74 views

Behavior of Ortho- and Para-hydrogen in a Magnetic Field

At low enough temperature, at equillbrium, the dihydrogen molecule is predominately parahydrogen, with the spins of the two protons opposite. Does an external magnetic field alter the ortho-para ...
1
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0answers
102 views

The classical hydrogen atom

Suppose we want to analyze a hydrogen atom using purely classical mechanics. This obviously is not exactly how things work - quantum mechanics plays a huge role and probability distributions are ...