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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1answer
58 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
57 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
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1answer
37 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 ...
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". ...
0
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2answers
34 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
585 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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3answers
152 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 ...
1
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1answer
174 views

Size of hydrogenic atoms

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 ...
2
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1answer
103 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 ...
3
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2answers
329 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 ...
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1answer
38 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 ...
0
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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?
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 ...
0
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1answer
26 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 ...
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2answers
115 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 ...
1
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0answers
27 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 ...
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2answers
244 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: ...
7
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3answers
2k 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. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
0
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1answer
156 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
2
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3answers
264 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
36 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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2answers
2k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
1
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1answer
64 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: ...
6
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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 ...
0
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2answers
66 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
32 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.
7
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2answers
456 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' ...
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2answers
110 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 $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
0
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2answers
73 views

Photon propagation direction prediction possible after interacting with neutral hydrogen?

My current line of research deals a lot with hydrogen's Lyman-alpha emission and subsequent interactions of the Lyman-alpha photons with the surrounding hydrogen gas. My question is whether ...
1
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1answer
120 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
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1answer
70 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
28 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
133 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
102 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 ...
0
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4answers
4k views

Collision between electron and proton?

What would happen if an electron collided with a proton such that the two do not collapse? Would the two become a unit, or would some force prevent them from bonding thus forcing the electron to orbit ...
1
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0answers
98 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
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1answer
96 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 ...
0
votes
2answers
151 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 ...
3
votes
3answers
805 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 ...
-2
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1answer
97 views

Angular momentum Bohr's model

I have been trying to derive speed, radius etc. in hydrogen atom using Bohr's postulates and not neglecting the coulombic attraction on proton. I know that they will be revolving around their centre ...
1
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5answers
8k views

How does the electron jump across “gaps” in its orbital?

I saw on perhaps COSMOS, and have heard mention from other professors, that electrons sort of "teleport" or something, in their orbital and the quantum level. So looking at the orbitals for a lone ...
1
vote
2answers
300 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 ...
4
votes
1answer
535 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 ...
0
votes
1answer
546 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 ...
8
votes
3answers
734 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 ...
5
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2answers
278 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 ...
4
votes
4answers
261 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 ...