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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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Energy eigenvalue of hydrogen-like atoms using Laplace-Runge-Lenz vector

I have a basic question about a few calculations involving the quantum mechanical Laplace-Runge-Lenz vector. In classical mechanics there is the Laplace-Runge-Lenz vector, which for a hydrogen-like ...
Jonathan Huang's user avatar
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33 views

Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]

I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
Dayane's user avatar
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4 votes
1 answer
128 views

Is the factorization method of Hamiltonian related to the theory of Lie groups?

I was learning about algebraic methods to solve the H atom, when I came across the factorization method. It is mentioned in various textbooks, notes and papers, like the one from Infeld and Hull. I am ...
Po1ynomial's user avatar
1 vote
0 answers
23 views

Why do closed shells have a SOC split?

Why do the energy states of closed shells behave like in the one electron case? Imagine an atom with one electron in the $2p$ orbital. $l=1$ and $s=1/2$, so spin orbit coupling leads to two levels ...
mathematica_guy's user avatar
1 vote
0 answers
30 views

Can hydrogen aquire magnetic moment?

Is the orientation of the electron inside its orbit around the proton inside the hydrogen atom dependent of the proton spin orientation... (as the spins of the two particles are cancelled out.)So if ...
Krešimir Bradvica's user avatar
4 votes
1 answer
108 views

Hydrogen atom in a very strong magnetic field

An atom of hydrogen is placed in a very strong magnetic field. The magnetic moment of the orbit of the electron may either align with the external field or may oppose it. What will happen with the ...
question-asker's user avatar
1 vote
1 answer
80 views

Incorrect factor in radial wavefunction $R_{2,1}$ of hydrogen atom

First of all, let me state that this isn’t a homework question but rather my personal annoyance. I can provide a proof in the comments if you think otherwise. The general equation for radial wave ...
Mr. Science's user avatar
0 votes
4 answers
78 views

Can we use Internal Combustion Engine exhaust to give heat for electrolysis to get hydrogen from water, to be used as fuel in the ICE?

Can we use exhaust from an Internal Combustion Engine to provide heat for the process of the electrolysis (to get hydrogen from water). And then use the H2 as fuel for the ICE so we use very little ...
Kenny Chu's user avatar
1 vote
1 answer
51 views

Distribution of states of H$_2$ gas for a given temperature

How can I calculate the population distribution of vibrational and rotational states of H$_2$ gas, for any given temperature? I think the vibrational states are more important, since the rotational ...
Random_Astro_Student's user avatar
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0 answers
30 views

Electric dipole transitions: why is $\langle \vec{d} \rangle$ for stationary states 0 but not for superpositions?

We've learned in lecture about electric dipole transitions for hydrogenic atoms, and our professor claimed that $\langle\vec{d}\rangle=0$ for stationary states, but not for superpositions of states. ...
JBatswani's user avatar
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Evaluation of $\langle nlm|\frac{1}{r^2}|nlm\rangle$ [closed]

I am trying to prove that $$⟨nlm|\frac{1}{𝑟^2}|nlm⟩=\frac{1}{𝑛^3*𝑎^2*(l+\frac{1}{2})}$$ (where $𝑎$ is the Bohr radius) for the $|𝑛𝑙𝑚⟩$ state of hydrogen. I know how to do this using Hellmann–...
Keith Duong's user avatar
9 votes
3 answers
839 views

Can the protium nucleus be in an excited state?

An electron in protium can absorb a photon and jump to an orbit of higher energy. Is an analogous procedure possible for the nucleus of protium (a single proton)? Can this nucleus be in an excited ...
azerbajdzan's user avatar
0 votes
1 answer
108 views

Positronium radius more than expected

I am trying to derive the basic properties of positronium. Usually it is stated that we can just set reduced mass of hydrogen atom as $\dfrac{1}{2}m_e$ and obtain: \begin{equation} r_n=\dfrac{8\pi\...
Aslan Monahov's user avatar
1 vote
1 answer
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Expectation Value Involving $s$-Wave Solutions to Central Potential

I previously posted a question regarding the expectation value described below, but it was closed because the question was not developed enough. Since I was given the option to delete it, I deleted it;...
StackUser's user avatar
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1 answer
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Hydrogen under pressure and high temperatere released energy: what is this process? [closed]

I am given hydrogen that is put into some pressure and high temperature conditions. After this it was found out that mass has decreased. It was also found that energy was released. Can someone, please,...
renathy's user avatar
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1 answer
118 views

Binding energy of Hydrogen = 0 = 13.6 ${\rm eV}$? [closed]

I was solving nuclear physics today.I used the binding energy formula on hydrogen.I found that B=0.But,B is also,as mentioned in my textbook,13.6eV. How?
CODE_FOR_PURSUIT's user avatar
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1 answer
55 views

Fusion in the sun for 4 hydrogen to Helium-4. How is the energy produced

So please correct me if I am wrong but: First 2 proton’s (each with an electron) fuse together, The mass stays the same so no energy is produced? Then 1 of the protons turns into a neutron with a ...
Bobbie Space's user avatar
3 votes
1 answer
79 views

Is metallic hydrogen solid or liquid?

If I squeeze hydrogen superhard with 400-500GPa of pressure, it becomes metal so is that solid or liquid? I know gallium melts on my hand and it's metal.
user6760's user avatar
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2 answers
77 views

How can we estimate the frequency of the spin-flip transition?

I was reading the Hydrogen line explanation on Wikipedia when my attention was caught by the following sentence: This transition is highly forbidden with an extremely small transition rate of $2.9×10^...
Mark's user avatar
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0 answers
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Applying Kato-Rellich to the hydrogen atom model to prove stability of first kind [closed]

Trying to Understand the lower bound on the Schrodinger Operator of the Hydrogen atom. Using the kato-rellich theorem. My education has been in physics and i am slowly adding to my mathematics toolset....
Gedankenhooman's user avatar
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1 answer
55 views

Is the axis of symmetry of electron orbitals arbitrary? Can it rotate?

The radial wavefunctions of electrons in hydrogen atoms, the electron orbitals or "clouds," is a topic covered in almost any quantum mechanics course or textbook. Something that has always ...
YaGoi Root's user avatar
1 vote
0 answers
28 views

Can hydrogen be stored in the crystalline structure of ice?

I recently read that when ice freezes to form hexagonal crystals, the space within the hexagon is in fact a vacuum. Could this space potentially be used to store burnable hydrogen gas? If so, would ...
Robert Goddard-Wright's user avatar
3 votes
2 answers
212 views

Why does $[Q,P]=i\hbar$ work for fermion? Shouldn't fermion satisfy anticommuting relation?

For hydrogen, we use $[Q,P]=i\hbar$ for electron, which is a fermion. Does it have a deeper reason such as that we're really considering the proton + electron system, which might be of bosonic nature?
Bababeluma's user avatar
1 vote
0 answers
19 views

Antisymmetry of the total molecular wave function in case of orthohydrogen

If my understanding is right, the total wave function of any system containing electrons and protons (and any other fermions for that matter) must be antisymmetric under exchange of the respective ...
QuantumQuasar's user avatar
3 votes
1 answer
92 views

Pauli exclusion principle in case of the $H_2$ molecule

Why do electrons in an $H_2$ molecule have opposite spins, while protons do not necessarily exhibit this behavior? Considering that both are fermions, shouldn't they both adhere to the Pauli exclusion ...
QuantumQuasar's user avatar
1 vote
0 answers
58 views

When will an electron fired at a proton be captured instead of scattered?

Suppose electrons of energy $E>0$ are fired toward a proton. Since energy is always conserved in a central motion, and because an electron bound to a hydrogen atom must have negative energy $(E<...
Solidification's user avatar
5 votes
1 answer
159 views

Is $n=1/2$ a valid hydrogen wavefunction?

The radial Schrodinger equation for the hydrogen atom is given by: $$\frac{1}{R}\frac{d}{dr}\left[r^2 \frac{dR}{dr}\right]+\frac{2m_e}{\hbar^2}\left(Er^2+ke^2r\right)=l(l+1).$$ Following the Bohr ...
John Eastmond's user avatar
0 votes
1 answer
102 views

Moments of hydrogen orbitals/Transition dipole moments

I'm interested in calculating transition dipole elements for atomic transitions. This means I would like to calculate things like $$ r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle $$ ...
Jagerber48's user avatar
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How can I calculate the column density of Hydrogen of a galaxy?

I have the following data: Mass of HI of the galaxy and radius. I thought using the following equation: $N_{HI} = \int n_{HI} ds \quad$ where the number density would be $n_{HI} = \frac{M_{HI}}{m_H V}$...
MJ_'s user avatar
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2 votes
1 answer
104 views

Why would a hydrogen atom form if proton and electron are left to attract each other, when they are very near? [closed]

In this question the OP asked, if electron and proton ,which are very near to each other,are left to attract in a straight line then what will happen? The answer was that a Hydrogen atom will form. ...
SacrificialEquation's user avatar
3 votes
0 answers
101 views

Strange fine structure splitting of the two-body Dirac equation

This question is a follow-up of the discussion about one of my answers. Marsch proposed a two-body Dirac equation for hydrogen in order to treat the proton recoil effects in a non-perturbative way (...
dennismoore94's user avatar
11 votes
1 answer
1k views

How is the proton accounted for in the relativistic solution of the hydrogen atom?

In the non-relativistic limit, the Schrodinger equation for the hydrogen atom can be solved using reduced mass techniques to account for the motion of both the electron and proton. I am wondering if a ...
Ghorbalchov's user avatar
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22 votes
3 answers
2k views

Does free neutron decay create a hydrogen atom?

When a free neutron decays, it is transformed into a proton, an electron, and a neutrino. Does this electron begin to "orbit" the proton, forming a hydrogen atom? Or does the electron run ...
Robert Goddard-Wright's user avatar
1 vote
1 answer
391 views

How is there so much ionized hydrogen in the sun?

To my understanding, the sun contains large amounts of ionized hydrogen compared to the amount of hydrogen in the first excited state. I am curious about the explanation, at the quantum scale, for how ...
Relativisticcucumber's user avatar
0 votes
0 answers
68 views

"Good" eigenstates for hydrogen atom in first excited state in an electric field

Consider a hydrogen atom in the first excited state that is being kept in an external electric field of strength $\lambda E_{ext}\mathbf {\hat{k}}$ . This electric field causes the splitting of the ...
Muralidhar Rao's user avatar
-1 votes
2 answers
98 views

Why can we ignore other charged particles when dealing with the Hydrogen atom?

Introductory treatments of the Hydrogen atom use the following Hamiltonian: $$H=\frac{|\textbf{p}_p|^2}{2m_p} +\frac{|\textbf{p}_e|^2}{2m_e}-\frac{Ke^2}{|\textbf{r}_p-\textbf{r}_e|}$$ However, given ...
Pol's user avatar
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-1 votes
1 answer
70 views

Quantum Collapse during the Measurement of the spectrum of hydrogen [closed]

We have hydrogen inside a tube, and we induce a voltage on it; a current passes through it and light is emitted. The frequencies of light correspond to the differences of the eigenvalues of the energy ...
Zatrapilla's user avatar
2 votes
1 answer
126 views

Can Gravity alone produce a simple Hydrogen or Helium atom?

Imagine there is no EM or Nuclear Force, and Gravity is the only force. Can gravity alone produce an atomic structure similar to a basic atom? In this scenario, the nucleus is just a single particle. ...
kvi's user avatar
  • 21
3 votes
3 answers
3k views

Why is there an exponential in the radial component of the hydrogen electron orbital wavefunction?

The solution for the Schrödinger equation for an electron in a (spherically symmetric) potential well shaped like $V=1/r$ is described by a wave function of the form $\Psi_{nlm}(r, \theta, \phi) = R_{...
acdr's user avatar
  • 243
1 vote
2 answers
193 views

What is the interpretation of these hydrogen probability density diagrams?

In the diagram above, what is the interpretation of all of the individual renders? Does the hydrogen atom continuously change between these states? For example, will $(n, l, m_l)$ become $(2, 0, 0)$ ...
JBatswani's user avatar
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0 votes
1 answer
105 views

Darwin Term (Fine Structure) and the Taylor expansion of the electric potential energy

I am trying to derive the Taylor expansion for the potential $U(\vec r + \delta \vec r)$. The general expression for the Taylor expansion is: $$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n....
imbAF's user avatar
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0 votes
1 answer
96 views

Linear Stark effect in Hydrogen: Why do states $\langle 2,0,0|H_1|2,0,0\rangle$ and $\langle 2,1,0|H_1|2,1,0\rangle$ vanish?

I was reading sec. 10.4, example (4), about the 'Linear Stark effect in Hydrogen' in the book 'Quantum Mechanics: A Modern Development' by Leslie E. Ballentine (Also related to example (ii) in ch. 13....
Rasmus Andersen's user avatar
0 votes
1 answer
607 views

What is the entropy of a hydrogen atom?

What is the entropy of a hydrogen atom, a bound proton and electron? First attempt: The standard molar entropy of hydrogen gas is 130.68 $J \, mol^{-1} K^{-1}$ at $298 K$. $1 \, mol = 6.02214076×10^{...
Jackson Walters's user avatar
-1 votes
1 answer
216 views

How much information is in a hydrogen atom?

How much information is contained in a hydrogen atom (a bound electron and proton) at room temperature? There are bounds that set limits on the amount of mass/energy that can exist in a given region ...
Jackson Walters's user avatar
0 votes
1 answer
293 views

Symmetry of the hydrogen molecule wave function

Due to their overlapping wave functions, electrons in an $H_2$ molecule must posses opposite spins. The nuclei (two protons) on the other hand are far enough apart for the Pauli exclusion principle to ...
QuantumQuasar's user avatar
0 votes
2 answers
70 views

Are the protons in dihydrogen in the same quantum state?

The electrons in the hydrogen molecule experience the same potential and are thus in the same state, so the Pauli exclusion forces them to have opposite spins. Since the protons are identical by ...
TunaSandwich's user avatar
1 vote
0 answers
55 views

For hydrogen atom wave function, why eigenstate of Hamiltonian isn't only spherical harmonics if $H$ commutes with square of angular momentum? [closed]

I was reading quantum mechanics and I read about CSCO. So, commuting operators should share common eigen states, does that mean same eigen states? because in hydrogen atom wave function, Hamiltonian ...
Shuvajit Dutta's user avatar
0 votes
1 answer
134 views

How does the pressure inside a pipe drop for a compressible gas (hydrogen)?

It is about turbulent compressible fluid, in this case, hydrogen gas. I have hydrogen gas at Ti = 25 K, pi = 3 bars, and ṁi = 0.001 kg/s (so 2.214 m/s) at the inlet of the tube. The pipe is 12.7 mm in ...
Alike minute's user avatar
0 votes
0 answers
65 views

Hydrogen atom in void

We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world where there are only an electron and a proton. Several forces act on it: ...
Victor's user avatar
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0 votes
1 answer
84 views

QM - States with same orbital angular momentum quantum number but different magnetic quantum number are equiprobable

I'm studying the hydrogen atom. My professor says that in a spherically symmetric problem, the choice of the $z$-axis is arbitrary and so, given a fixed value of the orbital angular momentum quantum ...
Tom Avery's user avatar

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