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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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0answers
134 views

Does separation of variables find all solutions to the 3-dimensional spherical time independent Schrödinger equation for a hydrogen atom?

I understand why it's OK to separate $\mathbf x$ and $t$ in the time-dependent equation. What's not clear to me is why, in the case of the 3-dimensional hydrogen atom, it's sufficient to find ...
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1answer
211 views

Evaluation of hydrogen atom matrix elements

Consider the operator $$\mathcal{P}=L_y L_z$$ and the hydrogen atom states $\left|n,l,m\right\rangle$. Evaluate the ratio $$\mathcal{R}=\frac{\left\langle3,1,-1|\mathcal{P}|3,1,0\right\rangle}{\...
2
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0answers
239 views

Accidental degeneracy in Hydrogen Energies [duplicate]

The energy of Hydrogen electron ground state should depend on $n$ and $\ell$, but it only depends on $n$. What is the reason behind this accidental degeneracy; I know that the reason lies in symmetry; ...
2
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1answer
211 views

Shape of Hydrogen atom in excited state with nonzeros angular momentum

Solution of Schrödinger's equation for an Hydrogen atom is well known: $$\Psi_{n,l,m} (r, \theta, \phi) = N e^{\frac{-r}{n r_1}} R_n^l (r) P_l^m(cos \theta) e^{im\phi} \,.$$ If we interested with ...
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2answers
70 views

A confusion about the naming of orbitals and the values of magnetic quantum number

From physics courses, I'm told that (for Hydrojen atom only), for a given $\vec L$ of the electron, $$|\vec L| * cos(\theta) = m_l,$$ where $\theta$ is the angle between the magnetic field and the ...
2
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5answers
317 views

Excitation of hydrogen atom by visible light

Question statement: A beam of light having wavelengths distributed uniformly between 450nm and 550nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the ...
1
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2answers
190 views

Is it possible for liquid metallic hydrogen to be present in a star

Liquid metallic hydrogen can form at extreme temperatures and pressures like that in the center of Jupiter and Saturn. I was just curious since some of the conditions can occur on stars is it ...
7
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2answers
1k views

Why doesn't the ${\rm H}_2$ molecule have a permanent dipole while the neutral ${\rm H}\,{\rm\small I}$ has one?

According to the National Radio Astronomy Observatory, the $21\,{\rm cm}$ line of hydrogen can be emitted by the neutral hydrogen atom due to the magnetic interaction between the spins of the proton ...
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2answers
226 views

Perturbation of relativistic hydrogen

Is there anyone that can provide a source for a relativistic hydrogen atom that is placed in a finite potential well? I am trying to find the new ground state energy for a relativistic electron that ...
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1answer
175 views

Hydrogen wave function stationary state [closed]

An electron in a hydrogen atom at an instant $t=0$ have the following wave function: $$\Psi(r,\theta,\phi,t=0)=\frac{1}{2}R_{1,0}(r)Y_0^0(\theta,\phi)+\frac{i}{\sqrt{2}}R_{2,1}(r)Y_1^0(\theta,\phi)+\...
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2answers
148 views

21cm line of Hydrogen spectrum [closed]

What is the advantage that we have when we study about 21cm line of Hydrogen spectrum over others, in radio-astronomy?
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1answer
103 views

Degeneracy split in $n=2$ hydrogen due to uniform electric field. Why is main diagonal zero?

I was checking about the stark effect in the hdyrogen in this site for $n=2$. Now, there are four states to deal with, $\psi_{200}, \psi_{21-1}, \psi_{210}, \psi_{211}$. The perturbation hamiltonian $...
8
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1answer
867 views

Can a quasiclassical electron wave packet in elliptic orbit be formed from bound hydrogen-like eigenstates?

Position probability densities of eigenstates of hydrogen-like systems have axial symmetry, so that the wavefunction too much resembles the circular orbits in Bohr's model. I'd like to have a ...
0
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0answers
92 views

state transition in the hydrogen atoms

Weinberg, in Lectures on quantum mechanics (p. 46) mentions that the transition rate for the hydrogen atom to decay from a state $\psi$ to a state $\psi'$ is proportional to $\left|\intop \psi'X\psi\...
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3answers
768 views

Why can't we harness the energy from neutron + protium = deuteron reaction?

The answer to this physics se question, established that 2.2Mev (Mega electron volts) of energy is emitted as a gamma ray photon when the hydrogen atom nucleus oka protium absorbs a slow moving free ...
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2answers
133 views

Hydrogen in a box

I would like to approximate the 1S wave function of a system constrained to a box $\{(x,y,z)|x\in[0,a],y\in[0,b],z\in[0,c]\}$, subject to the potential of the hydrogen atom. I have proposed the ...
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2answers
1k views

Proof of Orthogonality of Hydrogen Atom Wave Functions

How can one formally prove the orthogonality of hydrogen atom wave functions? I understand how the angular part is orthogonal, and I know that the radial part is orthogonal iff the quantum number $l$ ...
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1answer
122 views

What happens if the bound electron of hydrogen atom gains kinetic energy exceeds binding energy?

Say a hydrogen atom is accelerated so that both the nucleus and the bound electron gains kinetic energy exceeding it's electron binding energy, yes I know an hydrogen atom with 1 proton, 1 neutron and ...
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1answer
785 views

What are the boundary conditions for the electron in a hydrogen atom?

From what I understand, the wave equation for an electron can be constructed using the "particle in a box" model in three dimensions. However, what would be the boundary conditions in this case? In ...
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1answer
68 views

How many different types of energy can a particle have? [closed]

I was just wondering if somebody could tell me if my reasoning here is correct: An atom or molecule as a whole can have three types of energy: translational, rotational, and vibrational. If the atom ...
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2answers
299 views

Hydrogen Atom Angular Momentum

It is stated in "Modern Physics" by Tipler and Llewellyn (pp. 284-285) when discussing the quantum numbers of the Hydrogen atom: Note the perhaps unexpected result that the angular momentum vector ...
3
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1answer
140 views

GNS construction for the Schrödinger's hydrogen atom

Does anybody know if the H-atom (no spin, no special relativity) has been treated in the literature starting from the axioms of QM by I.E. Segal? These axioms are: We call a structure $\frak{A}$ ...
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1answer
551 views

Rydberg constant

I derived the Rydberg constant with the help of Bohr model but I read on the internet that we have to assume the mass of nucleus to be infinitely larger than the electron's. However, I got the answer ...
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1answer
249 views

What happens when a neutron is absorbed by a regular protium hydrogen atom?

Light Water Nuclear Reactors (LWNR) need enriched uranium fuel rods since the light water coolant tends to absorb in addition to moderating neutrons. What happens when a regular hydrogen atom, just ...
0
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1answer
58 views

Is the electromagnetic field static or does it oscillate around a hydrogen atom?

From the wave-particle duality we know that the electron can be viewed as both a particle and a wave. One example is that electron can be seen as a standing wave around an atomic nuclei. What would ...
2
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1answer
81 views

Hydrogen as energy storage

How viable is hydrogen as an energy storage medium? It would be extremely easy to split water into hydrogen and oxygen . It also has high energy content so relatively a large amount of energy can be ...
3
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1answer
749 views

What is the physical significance of the overlap integral?

What is the physical significance of the overlap integral in the covalent bond formation (say, the $H_2$ molecule)? as far as I can understand, even if the overlap integral is zero, the Heitler-...
2
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2answers
283 views

What would be the “waste product” of metallic hydrogen combustion?

It is thought that Metallic hydrogen would make a better rocket fuel that ones we currently have. I wonder, what are the waste products of its combustion? Would it be correct even to call it ...
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0answers
660 views

Exact Fourier transform of Hydrogen atom wavefunction in 3D position space

From wikipedia we know that the bound state wavefunction $\Psi_{n\ell m}(\boldsymbol{r})$ for the hidrogen atom in position space $(\mathbb{R}^3)$ with spherical coordinates $\boldsymbol{r}=\{r=|\...
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0answers
331 views

What is the difference between Lamb shift and the Darwin term?

I am currently learning for an exam and I wonder what the difference between the Lamb shift and the Darwin term is. What I know is that the Darwin term affects only the s-states of the hydrogen atom ...
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1answer
74 views

Which spectrum of hydrogen is predicted by Maxwell's equations? [closed]

Which spectrum of hydrogen is predicted by Maxwell's equations? Assuming no Lorentz force, or protons and electrons are forced to not crush on each other and be at the right distance apart. Was this ...
0
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2answers
468 views

Quantization of Angular momentum with Bohr model versus solving the Schrödinger equation [duplicate]

Looking at an hydrogen atom with the bohr model we get $$L=n\hbar, \qquad n\in\mathbb{N}\tag{1}$$ for the angular momentum. But by solving the Schrödinger equation, we get $$L=\hbar\sqrt{\ell(\ell+...
3
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1answer
178 views

Why does the Lamb shift only affect s-states?

The shift is due to interactions between atomic electrons and vacuum state fluctuations, so I would think that there would be an associated energy shift for all states, and not just s-states. Also, ...
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1answer
122 views

Calculating Darwin Term for Hydrogen

The standard classical approximation of the Darwin term in hydrogen's fine structure goes something like this. We approximate the 'smeared' potential due to the electron's fluctuating position as $V(\...
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0answers
141 views

Is there a way to quantify the entanglement in a hydrogen atom?

It is known that whenever the Hamiltonian contains an interaction part, the two interacting subsystems are entangled, thus an electron is surely entangled to a proton in a hydrogen atom. The ...
0
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1answer
189 views

Why does the separability of the hydrogen wavefunction vary under different reference frames?

I know that two particles are entangled when their Hamiltonian contains an interaction part, but it seems to me that for the ground state of the hydrogen atom $\frac{1}{\sqrt{\pi}}\left(\frac{1}{a_0}\...
2
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1answer
196 views

Momentum of a hydrogen system is imaginary. Why?

The hydrogen ground eigenstate: $$ \psi(r) = \frac{1}{\sqrt{\pi r_0^3}}\exp\left(\frac{-r}{r_0}\right) $$ Notice how nice: $$ \frac{\partial \psi}{\partial r}(r) = \frac{1}{\sqrt{\pi r_0^3}}\frac{-1}{...
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1answer
24k views

Relation of potential energy and total energy in Bohr Model of the hydrogen atom

I am currently in the 11th grade. In the Bohr Model of the hydrogen atom, potential energy is two times that of total energy. It means that magnitude of potential energy is two times that of magnitude ...
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1answer
288 views

The hydrogen atom, Legendre and Laguerre equations

I was looking for the solution of the Schrödinger equation for the hydrogen atom and I found that the angular component of the solution is: \begin{equation} \frac{1}{sen\theta} \frac{\textrm d}{\...
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2answers
1k views

Classical force keeping electron in orbit around proton in hydrogen atom [closed]

In terms of Classical Physics, what force would be required to hold an electron in orbit around a proton, i.e., an hydrogen atom? I have done a calculation, but need verification.
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2answers
39 views

Data supporting abundance of H and He in universe

I am a science educator, writing a lesson sequence for students on understanding evidence that supports the big bang theory. I am trying to figure out whether there is accessible galaxy spectral DATA,...
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1answer
951 views

Spin-orbit coupling, degeneracy of eigenvalues

I just read in a book about atomic physics that an important part of the fine structure of hydrogen is spin-orbit coupling. The Hamiltonian of spin-orbit coupling in the hydrogen atom is given by $$H_{...
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2answers
138 views

Why the solutions of Schrödinger hydrogen atom equation do not involve $U$ or $E$?

Please tell me if I am wrong. The general solution to 3D Schr Eq. does not have the terms $U$ or $E$. So the positions of electrons are total independent of the function of potential energy? $$\dfrac{...
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0answers
131 views

Orbitals of hydrogen, superposition

I'm trying to find the time evolution of the following superposition states in the hydrogen atom: $$\psi_- = \frac{1}{\sqrt{2}}\left(\psi_{1,0,0}+\psi_{2,1,-1}\right) \\\psi_0 = \frac{1}{\sqrt{2}}...
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1answer
637 views

How to find hydrogen wave-functions?

I have found the hydrogen wave functions and would now like to calculate the function that describes the orbitals so that I can plot this function and see how they look. I don't know how I can do ...
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0answers
46 views

What are the discrepancies of Dirac's hydrogen fine structure?

Hansen's experimentally proved five components of H_alpha line. Sommerfeld's relativistic correction was able to show only three components theoretically. Dirac took into account spin orbit ...
5
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1answer
361 views

Intuitively, why is the energy decrease of the singlet state three times larger than the energy increase of the triplet state (hyperfine correction)?

Following Griffith's Hyperfine Splitting section for the Hydrogen atom, he concludes that the energy decrease for the singlet configuration is 3 times larger than the energy increase for the triplet ...
0
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1answer
126 views

Why is there no Sigma-minus ground state for molecular hydrogen ion?

I'm studying a bit of molecular physics and having some trouble understanding the +/- symmetry in a simplest molecule like a molecular hydrogen ion (2 protons and 1 electron). In a book, usually they ...
1
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0answers
107 views

Time dependent perturbation from Galilean transformation

I'm having a little trouble figuring out how to start this. The question is as follows. At time $t<0$ a hydrogen atom is in the rest frame $\mathfrak{R}$. Then at time $t=0$ the atom suddenly ...
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2answers
625 views

What is the significance of Hydrogen column density?

I have always read in the textbooks about star formation and ${\rm H}_2$ column densities. What is the relationship between the two? How is star formation affected by ${\rm H}_2$ column densities?