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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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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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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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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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96 views

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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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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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". ...
1answer
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 ...
1answer
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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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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1k 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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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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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 \delta E^{(2)}_{100}= -\frac{1}{4}a_o^3 E^2(4+5Z^...
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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 ...
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 ...