Questions tagged [hydrogen]

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 Equation. Hydrogen atoms are the only atoms which could exist even n a world with fine - structure constant 1.

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Physical meaning of $\langle nlm|\hat{z}|n'l'm'\rangle$

I'm working on a quantum mechanics problem with some friends and we're trying to make an argument using symmetry rather than maths. What would the physical interpretation of $\langle nlm|\hat{z}|n'l'm'...
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I am having a doubt in graphs of $4πr^2|\psi|^2$ vs $r$ and $4πr^2|R(r)|^2$ vs $r$

To show radial probability, in some sources they used the graph $4πr^2|\psi|^2$ vs $r$ In some other sources, they used the graph $4πr^2|R(r)|^2$ vs $r$ However, $\psi(r,\theta,\phi)=R(r)Y(\theta,\phi)...
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Maximizing probability or probability density

We are given the relation $dP=r^2|R(r)|^2dr$. Also, we are given $R(r)$ for the 1s orbital, and we are required to find the most probable radius of the electron in the 1s orbital of a hydrogen atom. ...
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Does the principal quantum number, $n$, have an operator?

The hydrogen energy eigenstates are labelled with well-defined $n$, the principal quantum number. Is there an associated operator than one can apply to these wavefunctions which would result in an ...
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Principles and methods of measuring the orbital angular momentum of $\rm H$-atom

When we talk about the orbital angular momentum (OAM) of the $\rm H$-atom, we mean the eigenvalues $l(l+1)\hbar^2$ of the OAM operator of the electron $\hat{L}^2$ defined from its classical ...
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How should get the expectation value of $1/r$ in the hydrogen atom? [duplicate]

I have a question of quantum mechanics. I want to calculate \begin{align}\left\langle \frac{1}{r} \right\rangle \end{align} in the state $n, l$ of the hydrogen atom. In the textbook I have, the ...
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Hydrogen Transitions in Foot

I was reading through Foot's Atomic Physics, and saw this depiction of the transitions of the hydrogen atom. My understanding is that here we must require $\ell - \ell' = \pm 1$. Indeed, this is what ...
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Could liquid hydrogen tank be any shape we want? [closed]

I am doing the initial design of an aircraft for my Aerospace Engineering project. I want to use liquid hydrogen as the fuel of my aircraft. However, a cylindrical fuel tank or spherical fuel tank ...
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How (if) are the hydrogen's "external" and "internal" wavefunction connected?

We can assign to a hydrogen atom an "internal" wavefunction: $$\psi(r,\theta,\varphi)=R(r)Y(\theta,\varphi)$$ We also assign an "external" wavefunction, describing the behavior of ...
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Quantum Central Force Problem and Angular Momentum

I am currently studying the quantum mechanics of the hydrogen atom. We have a proton and an electron orbiting around, so the Hamiltonian is: $$H=\frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+U(|\vec{r}_2-\vec{...
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Selection rules for electronic transitions in dipole approximation

I saw this video which provides a clear, though simple, introduction to the argument. I think the main thing missing is a proof for: $\Delta \ell = \pm 1 $ $\Delta m_\ell = 0, \pm 1$ $\Delta m_s = 0$...
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Why is the separation constant (used in obtaining the electron's wave function in hydrogen) a constant and not a function of position (and time)?

The Schrödinger equation for the hydrogen atom in polar coordinates is: $$ -\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \psi}{\partial r}\right) + \frac{1}...
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About the calculation of the Spin-orbit correction for the Hydrogen atom

I'm using first order perturbation theory to calculate the energy corrections due to the fine structure of the Hydrogen atom. I'm having some doubts about the calculation of the spin-orbit term. Some ...
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What is the experimental evidence for the hydrogen atom having a Coulomb potential?

It is famously impossible to deduce the shape of a drum from its spectrum, in general. In the case of the hydrogen atom, there are non-Coulomb potentials that produce the same spectral series! (See ...
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Magnetic field perceived by the electron

This section presents a relatively simple and quantitative description of the spin-orbit interaction for an electron bound to a hydrogen-like atom, up to first order in perturbation theory, using some ...
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How does protium-protium fusion work?

How does protium-protium fusion work? As far as I know, a proton turns into a neutron by emitting a positron. How does that work? Shouldn't a proton be slightly lighter than a neutron? This seems to ...
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Transparency of hydrogen to different electromagnetic wavelengths in the early universe

I can somehow grasp the early universe being compared as a sphere surface filled densly with plasma like a spherical chessboard all filled with chess pieces.So as that surface streched the distances ...
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Creation and annihilation operators in the hydrogen atom

In my quantum chemistry course, we have been discussing the wavefunctions of the hydrogen atom, further, I am familiar with the idea of ladder operators from the quantum harmonic oscillator. Can we ...
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Hydrogen atom: Estimation of binding energy from each force

I've been asked to give an estimation on the binding energy related to each fundamental force (gravitational, electromagnetic, weak and strong) for the Hydrogen atom (you know, the one with a single ...
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Metallic hydrogen production [closed]

Why is there such a big deal made about metallic hydrogen if it can't be made industrially? I mean, it's very hard to produce in a lab, and the samples produced are of very small quantity, so why are ...
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Laguerre diferential equation for the radial part of the Hydrogen atom

I am working on understanding the solution to the Schrödinger equation for the Hydrogen atom and I am now stuck on something concerning the Radial part of the equation. After the change of variables $\...
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When is the principal quantum number $n$ a good quantum number?

Since I don't know an associated operator to the principal quantum number $n$, I don't know when it is a good quantum number. By 'good quantum number' I mean a quantum number that is conserved over ...
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Is the precession in the vector model real?

The vector model often mentions various vectors 'precessing' in order to explain things such as spin-orbit coupling, B-field coupling and LS-coupling, but I'm not sure how literally this 'precession' ...
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Are $|n,l,s,j,m_j \rangle$ states exact energy eigenstates for one electron spin orbit coupling or just zero order approximations?

In my atomic lecture notes calculating the changes with spin-orbit coupling for a one electron atom they describe the $|n,l,s,j,m_j \rangle$ states as being used to 'diagonalise the spin-orbit ...
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Understanding the meaning of the integral of energy of an $\rm H$ atom

This is probably very basic but my notes are confusing and not clearly written so I would appreciate some help in trying to clarify the following points: If we consider the expression $$\left\langle \...
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How to "restrict to a subgroup" to explain representation structure?

I am reading from Quantum Theory, Groups and Representations - Woit. In Chapter 21, on page 237 in discussion of the energy eigenstates of the Coulomb potential, the following figure is presented: ...
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Is it better to think of electron shells as depending on the value of $n$, or depending on the energy difference between sub-shells?

Often electron shells are defined as 'states with the same principal quantum number $n$' which would suggest that $3s$, $3p$, $3d$ sub-shells are all in the same shell. Conversely, it is also often ...
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Bound state of Hydrogen atom at large $r$

When the radial equation of SE is solved for Hydrogen atom, to see the asymptotic behavior, we assume $r$ tends to infinity. The differential equation we are left with is: $$ d^2U/dr^2 = -\frac{2mE}{\...
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Hydrogen Atom in two spatial dimensions with $1/r$ potential [closed]

I am almost new to Quantum Mechanics. Recently I learned about the hydrogen atom in three dimensions. I struggle to answer the following exercise where the hydrogen atom in two dimensions is ...
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Origin of Spin-Orbit Interaction

The spin-orbit interaction in a hydrogen atom is often explained as arising from an interaction energy $U=-\mathbf{m}\cdot\mathbf{B}$ where $\mathbf{m}$ is a magnetic moment due to the electron’s spin ...
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Why ionization is more probable in hydrogen atom than excitation to the $n = 3$ level?

The Wikipedia article about the H$\alpha$ spectral line states "it takes nearly as much energy to excite the hydrogen atom's electron from $n = 1$ to $n = 3$ (12.1 eV, via the Rydberg formula) ...
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Can wavefunctions always be separated into a product of spatial and spin parts? [duplicate]

Firstly, I wanted to check. Can wavefunctions exist that are not in the form $\psi = \psi_{\mbox{spatial}}\times\psi_{\mbox{spin}}$? I am assuming you can have situations that are dependent on spin ...
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Could you survive on hydrox in at 10 atmospheres?

I was told that hydrox is incredibly dangerous, that pure oxygen will combust without any source of ignition at 3 to 4 atmospheres of pressure, and that because humans are hydrocarbons they will act ...
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Hydrogen radial wave function in Feynman

I'm reading the classical Feynman's lectures on hydrogen atom, and I want to calculate the radial component of the wave function with the formula (19.53) $$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\...
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About calculating a contribution to Lamb-shift through Uehling's potential

Well, I've been calculating Uelingh potential using the amplitude of the QED vacuum polarization. Now, I'd like to go on and calculate the Lamb-shift. And here is my question: How can I do that? ...
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Good quantum number for the weak field Zeeman effect

To find the fine structure of hydrogen using nondegenerate perturbation theory, we choose the eigenstates of L2, S2, J2, and Jz. As stated in Griffiths Introduction to Quantum Mechanics, the good ...
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Nuclear beta decay to hydrogen

In reading about nuclear beta decay: $$n \longrightarrow p + e^{-} + \bar \nu$$ It occurred to me that two of the particles resulting from this decay are the constituents of the hydrogen atom. So why ...
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Pauli exclusion principle for $H_{2}$

We know that depending on whether their spins are parallel or antiparallel, two electrons (each with spin ½) can combine to give a total spin of $1$ (parallel)or $0$ (antiparallel). But only one of ...
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Is the energy of an orbital dependent on temperature?

In the Schrodinger Equation's solution for electron orbital energy levels of the hydrogen atom there is no temperature dependency. $$ E_n = - \frac{m_{\text{e}} \, e^4}{8 \, \epsilon_0^2 \, h^2 \, n^2}...
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Cross section for Hydrogen molecule formation

I have been searching for theoretical articles that calculate the hydrogen formation cross section $\sigma(H+H \rightarrow H_2)$, but I found nothing. Can anyone suggest me articles or computer ...
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What is the most common method used to cool hydrogen below its boiling point?

I would like to know what methods companies/organizations/scientists use to cool gaseous hydrogen below its boiling point of ~250 degrees Celsius. I am a new student to thermochemistry and am not ...
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Another way for production of positive fusion

I am wondering why energy positive fusion cannot be produced in the following manner. Large tank of hydrogen pressurized to such a high a level it would push the limits of current technology. ...
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Hydrogen gas tube and the spectrum [duplicate]

Generally to detect the hydrogen spectrum people uses the hydrogen gas tube as a light source. My question is, since the gas in the tube is the hydrogen molecule $H_2$ why is the spectrum equal to the ...
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2 votes
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Balmer spectroscopic lines from plasma?

In stars, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 kelvins (spectral type A). Balmer series|Role in ...
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5 votes
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Can this matrix be evaluated with the help of the Wigner-Eckart theorem?

I wonder if the problem in the image can be solved with the Wigner-Eckart (W-E) theorem. These elements have to vanish. I tried introducing the identity operator in between $r$ and $p$ to then use the ...
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Franck and Hertz's experiment

The Bohr's model of the atom was defined only for hydrogen and hydrogen-like species. Yet, the Franck-Hertz experiment was performed with Mercury vapour- which, obviously, isn't hydrogen-like. What's ...
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Hydrogen-One (HI) Image and R-band

In the paper below, on page 3, it says "In the lack of HI image, we use the r-band b/a ratio to correct for the inclination". Am I correct in thinking that what this means is that if we ...
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What would happen if you tried to use oil as fuel in a fusion reactor? [closed]

At first, this question seemed silly, but there might be some sense to it. OpenAI's GPT algorithm suggested to me that using oil in fusion technology could be a breakthrough. I thought about it for ...
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Why do molecules form band spectrum?

If we observe any textbook they say that molecules form band spectrum. But a H2 molecule is just 2 H atoms and both form line spectra but somehow combination of 2 H atoms formed band spectrum. Because ...
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2 votes
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Why do the $d$ orbitals have such strange symbols?

Why are the five d-orbitals denoted by the symbols $d_{z^2}, d_{x^2-y^2}, d_{xy}, d_{yz}$ and $d_{zx}$? Does it have to do with the wavefunctions of d-orbitals? The symbols for the f-orbitals are ...
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