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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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 ...
2
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1answer
102 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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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 ...
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1answer
125 views

energy difference uniqueness in hydrogen atom

Is the energy difference between two energy levels unique for that particular pair of levels for a hydrogen atom ? If so how can one prove it?
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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". ...
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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 $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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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 ...
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0answers
113 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 ...
2
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0answers
99 views

Why is metallic hydrogen degenerate matter?

Why is metallic hydrogen considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force ...
2
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0answers
128 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
2
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0answers
110 views

Line-shape asymmetry in undergraduate Hydrogen-Deuterium experiment

I'm working as an LA (undergraduate TA) for an undergraduate physics laboratory experiment where students test the Bohr model and use reduced mass to determine the approximate mass of the neutron. In ...
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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 ...
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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 ...
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0answers
101 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 ...
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0answers
590 views

tritium beta decay - probability of being in 1s state

Hydrogen-like wavefunctions have the form: $$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}$$ $$Y_{00} = \frac{1}{\sqrt {4\pi}} $$ where $a_0 = \frac{4\pi \epsilon_0 ...
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0answers
253 views

Step in derivation of solution to Dirac equation for hydrogen

My text, when solving hydrogen in the Dirac equation, makes the claim $\varphi_{j m_j}^{(+)} = \frac{\mathbf{\sigma} \cdot \mathbf{x}}{r} \varphi_{j m_j}^{(-)}$ where $\varphi_{j m_j}^{(\pm)}$ are ...
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0answers
124 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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0answers
820 views

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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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 ...
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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.
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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 ...
0
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0answers
90 views

Greens function/resolvent of hydrogen Hamiltonian

Let $H$ be the Hamiltonian for the nonrelativistic hydrogen atom, i.e. $$H=-\frac{1}{2}\Delta-\frac{1}{r}$$ I am searching for an asymptototic expansion of the Greens function or respectively the ...
0
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0answers
28 views

Quantum mechanics for macroscopic charges?

OK first off tell me if my understanding of the following is correct: In a Hydrogen atom, one would expect that the opposite charges (electron and nucleus) to attract each other, according to ...
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0answers
112 views

Perturbation of a Hydrogen Atom in a Quadrupole Field

Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the ...