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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.

77 questions with no upvoted or accepted answers
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How can we deduce that a hydrogen atom is stable in relativistic QED?

Consider relativistic quantum electrodynamics (QED) with three quantum fields: the electromagnetic field $A_\mu$, one fermion field $\psi$ for electrons/positrons, and one fermion field $\psi'$ for ...
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245 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 "...
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Why does the Dirac equation work for the hydrogen atom?

The Dirac equation works well for predicting the spectrum of the hydrogen atom, famously incorporating relativistic effects like fine structure. Yet, there seems to be a sense in which this is ...
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292 views

Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
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Black hole nucleus in hydrogen

The hydrogen atom gets the spectrum it has because you analyze the Schrodinger equation in spherical symmetry with the potential given by $V=-\frac{1}{4\pi\epsilon_0}\frac{e^2}{r}$. Yet the same ...
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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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50 views

Diffusion of Hydrogen through Molybdenum alloy

I have been performing experiments to study the diffusion of Hydrogen through Molybdenum. According to Sievert's law diatomic molecules would diffuse as atoms. But according to my experiments I notice ...
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214 views

On Virial theorem and its Quantum mechanical analog

The relation established by the virial theorem is well pronounced in the case of potential energies that are power law functions of distance. In quantum mechanics, a similar analog is present, ...
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587 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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Can one add a discrete set of functions to complete the bound states of the hydrogen atom?

Though being an infinite orthonormal set of functions, the bound states $\Psi_{nlm}$ of the hydrogen atom do not form a basis of the Hilbert space $L^2(\mathbb{R}^3)$ due to the continuous spectrum, i....
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Why do low concentrations of H2 in He gas exhibit lower thermal conductivity than either?

Thermal conductivity of He+H2 mixtures, as a function of molar concentration of H2, exhibit a minimum at around 14% H2. See Fig. 2 below from "Thermal conductivity of the hydrogen-helium mixture". ...
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91 views

Has hydrogen ever been used in Quantum Computing?

What I'm talking about is hydrogen atom quantum dots, where a hydrogen atom is embedded in a semiconductor. The reason for asking is because the Hydrogen atom is a Quantum mechanical system with a ...
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86 views

How much UV does a hydrogen flame emit?

A hydrogen flame is invisible but emits ultraviolet (and infrared) radiation. How much UV does a hydrogen flame emit for a given reactant flow or a given heating power? Could a hydrogen flame be used ...
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50 views

Hydrogen energy state transition times and probabilites

How correlated is the energy absorbed to the later energy emitted, and hence to the transition type? What is the scale of time it takes to make a downward transition in energy level? In a very cold ...
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41 views

Why is the fine stucture not included in the energy correction for problems with external magnetic field?

In problems regarding the effect of an external magnetic field on a hydrogenlike atom, it is assumed that the total energy splitting of the $1s$ level is due to the hyperfine structure and the Zeeman ...
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138 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = \left\{\...
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499 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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Finding the probability that a $1s$ electron in ${}^3$H remains in the $1s$ state after beta decay to ${}^3$He with the sudden approximation

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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416 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 ...
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160 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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40 views

Does hydrogen gas laser exist? If not, why?

I have searched the internet, and this forum, but can't find a mention of hydrogen gas laser. There does, however, exist the hydrogen maser that used the 21cm radiation. Also there exist Nitrogen gas ...
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67 views

Can a hydrogen atom temporarily attract an additional electron to form a negative ion?

Negative ions should be a kind of temporary substance form that exists widely. Can a hydrogen atom temporarily attract an additional electron to form a negative ion? Other elements or molecules can. I ...
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50 views

Has man ever observed the spectrum of a single hydrogen atom?

Were there this kind of experiment done before? The spectrum we observed is radiated by huge number of hydrogen atoms in the gas, not by single hydrogen atom. I know it's very hard to test a single ...
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50 views

Are parahydrogen and orthohydrogen identical particles?

I have no formal physics background, just aerospace engineering, and I'm working on a DSMC project simulating relaxation of hydrogen in non-equilibrium, rarefied, 1D flow via translational and ...
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49 views

How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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1answer
174 views

Questions on Stark Effect on Hydrogen

Suppose that a hydrogen atom is subject to a weak uniform electric field $\vec{E}=\epsilon \hat{z}$. Let's neglect the effect of electron spin. The perturbation added to the original hamiltonian $H_0$ ...
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How do I proceed with the following coulomb integral?

I am trying to solve the $H_{2}^{+}$ ion problem using Fourier transform approach. The Hamiltonian that I am trying to solve is as follows, $$H=-\frac{\hbar^{2}}{2m_{e}}\nabla^{2}_{e}-\frac{e^{2}}{4\...
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65 views

Finding the expansion coefficients of the decomposition of a 3D Gaussian wavepacket in the eigenfunctions of the Hydrogen atom

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/...
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38 views

What are all the wavelengths of the dueterium spectra?

What are all the wavelengths in the spectrum of deuterium? I've searched and came up with an abstract that only lists the visible part of deuterium's spectrum (see http://myslu.stlawu.edu/~jmil/...
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44 views

How much electricity does it take to create hydrogen from water depending on the water's pressure?

Imagine creating bubbles of hydrogen and oxygen underwater at a particular depth using electricity. Then reusing the energy of the bubbles going upward to the surface ( buoyancy ). How is the energy ...
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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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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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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 ...
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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 ...
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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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151 views

What is meant by the Lyman alpha color temperature?

I understand the color temperature of radiation to be the temperature of a blackbody that has a similar spectrum as the radiation. I am puzzled by references in astrophysics to the Lyman-alpha color ...
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1answer
138 views

Hydrogen in an electromagnetic field bound states for full quantum electrodynamics

I am looking for a reference or derivation of the non-relativistic bound states of hydrogen in an electromagnetic field that include Zeeman effect, Stark shift, and Lamb shift. I am looking for a ...
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1answer
354 views

Using the Heisenberg Uncertainty Relation to Estimate Ground State Energies

In Shankar's Principles of Quantum Mechanics, he applies the HUP to estimate the ground state energy of the Hydrogen atom. In the proof, it is said that the first step to minimizing the expectation ...
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75 views

Is there a “complete” Hydrogen level spectrum diagram out there?

From basic quantum physics we know that the energy levels in Hydrogen are quantized, with the first steps being made with the Bohr model. Then, spin gets introduced, and we get spin-orbit coupling, ...
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113 views

Darwin term affecting hydrogen s-states

The Darwin term, a correction to the non-relativistic hydrogen Hamiltonian due to the zitterbewegung of the electron, is given by $$H_{Darwin}=\frac{e^2\hbar^2}{8m^2c^2\epsilon_{0}}\delta^3(\...
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435 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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507 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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167 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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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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Dependence of radial probability function on quantum numbers

I was reading the book "Quantum Physics" from Eisberg & Resnick about the expected value of the electron radial coordinate, which it defines as \begin{align} \overline{r_{nl}} = \int_{0}^{\infty}...
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Trying to solve TDSE for Hydrogen atom, but I cant determine initial condition

I am trying to solve TDSE for a hydrogen atom in the b-spline basis set. $$i\dfrac{\partial}{\partial t}\Psi(t)=[H_{0}+D(t)]\Psi(t)$$ with initial condition $\Psi(t=-\infty)=\Psi_{g}$, where $\Psi_{g}$...
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More than two linearly independent solutions to the (linear second order) radial wave equation?

I'm puzzled by the following radial wave equation: $$ \left(\frac{\hbar^2}{2m_r}\left(-\frac{d^2}{dr^2} -\frac{2}{r}\frac{d}{dr} + \frac{l(l+1)}{r^2}\right) + V(r)\right)R_{nl}(r) = ER_{nl}(r)$$ ...
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53 views

Where does this Differential Equation comes from?

Im studying Stark Effect and im trying to prove that the second order correction to the ground state of hydrogen like atoms goes like \begin{equation} \delta E^{(2)}_{100}= -\frac{1}{4}a_o^3 E^2(4+5Z^...
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21 views

Semi-classical Hydrogen Atom Angular Momentum under Magnetic Field

Suppose we have a semiclassical hydrogen atom in its ground state at the x-y plane with the proton being at the origin. Let there be a magnetic field $\vec{B}=B\hat{z}$. By deriving the orbital ...
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1answer
170 views

virial theorem hydrogen atom

I calculated $\langle T \rangle$ and $\langle V \rangle$ as a function of time of a given state of the hydrogen atom $|\psi\rangle=a|1,0,0\rangle+b|2,0,0\rangle$ and I found that $$\langle V \rangle ...