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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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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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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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How does the ratio of hydrogen to helium help prove the big bang theory?

From what I have read one of the key pieces of evidence for the big bang theory is the ratio of hydrogen to helium in the universe. I have not seen any explanation as to how the big bang theory ...
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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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About the size of the orbitals $s$, $p$, $d$, etc, in $H$ atom

Can we define a size for the H atom orbitals which are not spherically symmetric, e.g. $p, d$ etc? For example, is it meaningful to say that the $(n+1)p$ orbital is larger in its extent than $np$ ...
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Hydrogen: Whether it's a metal or non-metal

I know hydrogen is a non metal, but when I just study about some introductory elementary band theory I find the band structure of hydrogen has a half filled valence band just like alkali metals, and ...
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Why is the “fine structure” correction called that way?

I'm working on the fine structure correction to the Hydrogen atom. I have more of a conceptal, maybe historical question, why is this correction called this way? and why is the fine structure constant ...
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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 \begin{equation} \delta E^{(2)}_{100}= -\frac{1}{4}a_o^3 E^2(4+5Z^...
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Why hydrogen lines are less visible in the Sun spectrum than in supernovae clouds?

Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those ...
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Question about Electric Dipole Transition Selection Rules [duplicate]

I learned that the selection rules for electric dipole transition in a hydrogen-like atom is \begin{align} \delta l & = \pm1 \\ \delta j & =0,\pm1 \\ \delta m_j & =0,\pm1 \end{align} I ...
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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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Expectation value of $x,y,z$ for general $nlm$ state of hydrogen atom

How to calculate expectation value of $\langle x\rangle, \langle y\rangle,\langle z\rangle$ for the general $\psi_{nlm}$ state? $x$ has $\sin(\theta)\cos(\phi)$ angular part which can be expressed as $...
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Can hydrogen plasma react with oxygen?

What if you put hydrogen in a vacuum and turned it into a plasma? There is no oxygen in the vacuum, but once you eject the plasma would it react drastically with the oxygen? Would it explode? Would ...
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Quantum energy levels of a point mass rotating about a fixed point

The question is: A particle of mass m is attached to a fixed point in space by a massless rigid rod of length a and can freely rotate about this point. Find the quantum energy levels of the system. ...
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Probability of finding hydrogen atom in its ground state given an initial state

So I came across this question that asked what is the probability of a hydrogen atom which is prepared in an initial state $\Psi (\vec{r},t)$ to be in the ground state $\psi_{100}(\vec{r}) =2exp(-r)Y_{...
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Plasma inside deuterium spectrum tube?

Hullo, In a deuterium spectrum tube there is a thin capillary in the middle (see picture) that glows purplish sort of. Now, I wonder what this glowing part actually consist of? Is it a completely ...
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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 ...
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Is the $2p\rightarrow2s$ transition possible?

Selection rules in one electron atoms are: $\Delta n=$ any $\Delta l=\pm1$ $\Delta m_l=0,\pm1$ $\Delta s=0$ Parity must change Under strong spin orbit interaction: $\Delta j=0,\pm 1$, but $j=0\...
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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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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 ...
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Finding the value of $r$ for which the radial function, $P(r)$, has a maximum? [closed]

In my (university) particle physics course, I am asked to find the values of $r$ for which the function $P(r)$ of a $2s$ Hydrogen electron has its maximum values. Here, $r$ denotes the distance in ...
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Radial term in the spin-orbit coupling

The spin-orbit interaction for the hydrogen atom is of the form $\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$ Now in my course, we treated this interaction by working in the basis of ...
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Symmetries of a differential equation, its solutions and hydrogen atom

A symmetry of a differential equation need not be shared by its solutions. However, under that symmetry, the one solution goes to another. For example, consider the time-independent Schrodinger ...
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How does the hydrogen atom actually “look like”? [duplicate]

When deriving the solutions for the "simple" quantum mechanical hydrogen problem, one normally uses spherical coordinates $(r,\theta,\phi)$, since the problem has rotational symmetry. The solution has ...
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44 views

Transitions in Hydrogen Atom

Suppose we have a Hydrogen atom in a superposition of the 1s ground state, $\psi_1 = R_{1,0}(r)Y_{0,0}(\theta,\phi)$, and the $m_l = 0$ state of the 2p configuration, $\psi_2 = R_{2,1}(r)Y_{1,0}(\...
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$\langle r \rangle$ and orbital energy [duplicate]

Even though $\langle r_{2s} \rangle > \langle r_{2p} \rangle$ based on the following formula $$ \langle r_{n\ell} \rangle = \frac{{a}_{0}}{2}(3{n}^{2}-\ell(\ell+1)) $$ $2s$ has a lower orbital ...
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Relativistic hydrogen wave function for python/mathematica

Is there any library/module for mathematica or python that has the exact solution of the Dirac equation for a hydrogen atom implemented? Sympy has the wave functions the non-relativistic wave ...
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Understanding the radial distribution function [duplicate]

I am confused why the maximum of the radial distribution function for 2p orbital is closer to the nucleus than that for 2s orbital. Doesnt this mean that there is a higher chance of finding 2p orbital ...
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Difference between radial distribution function and probability density function

I want to be clear on the difference between radial distribution function ${P}_{nl}(r)dr$ and probability density function in the context of hydrogen wave function. Definition of ${P}_{nl}(r)dr$ is ...
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Expectation value of coordinate mixed operator with ground state

I have a Hamiltonian of the Hydrogen atom: $H=H_0+H_1+H_2$ , when: $H_0 $ is the hamiltonian from central force and from electron momentum , $H_1$ is the relativistic kinetic fixing, and $H_2$ is the ...
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Is there a mass spectrometer software that can measure the mass of a hydrogen atom [duplicate]

For a school project I need to measure the mass of a hydrogen atom either as a lab experiment or with a computer simulation. Since I don't have the appropriate equipment for the experiment, does ...
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29 views

Is metallic hydrogen an example of exciton?

I know that in exciton an electron is excited and goes from valence band to conducting band leaving an electron hole which is positively charged, soon Jupiter came into my mind and then this question. ...
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Why does $2p$ have highest RDF at $4a_{0}$?

I was reading notes from my first class in Quantum Physics that I received and left confused at the following statement: For each principal quantum number $n$, the orbital set with the highest $\...
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What is the resistivity of solid non-metallic hydrogen?

If I were to use solid hydrogen (assuming temperature of 10K, pressure 1 atm) as a resistor of sorts, what would it's resistivity be? (Note: If someone can give me a good resource on info like this ...
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What are the boundary conditions for the Hydrogen Atom which cause the polar power series to need to terminate?

I am trying to solve the Hydrogen Atom, and I am stuck in the polar equation. To simplify, I have taken the special case in which $m=0$ to get the Legendre Equation: $$(1-x^2)P''(x)-2xP'(x)+AP(x)$$ $$(...
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82 views

Lamb Shift and virtual particles [closed]

Can someone explain about the Lamb Shift?
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430 views

What is the meaning of natural line broadening?

I have recently found one exercise in an exercise book: During the transition from the first excited state of a hydrogen atom into the ground state, photons with a wavelength of 121.5 nm are ...
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1answer
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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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56 views

What is the point of talking about three axes for hydrogen orbitals?

The hydrogen orbitals are usually described using polar coordinates ($\Psi(r, \theta, \varphi)$). I understand that $r$ is the distance from the center of the atom, but how are the angles defined? ...
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1answer
57 views

Relation of Hydrogen orbitals to its spectral series?

I'm looking for the link between the Rydberg formula for hydrogen spetcral series $$\frac{1}{\lambda_{\mathrm{vac}}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ and this image. Is it right to ...
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170 views

What is the current measured (i.e. model independent) density of hydrogen $H$ in the universe?

The question came up in this thread: What is the current value for the temperature at which Recombination took place? I was under the impression that we had an independent measurement of Hydrogen in ...
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32 views

Assignment of $m_\ell$ values to $p_x, p_y$ and $p_z$ states

For the orbital angular momentum quantum number $\ell=1$, there are three possible $m_\ell$ values, namely, $-1,0$ and $+1$. Which $m_\ell$ value is associated with which of the three p spates, namely,...
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Resistance to a nanoscale system like hydrogen atom? [closed]

Can we talk about the resistance to a nanoscale system? For example, the hydrogen atom. It is obvious that the conventional resistance formula $$R=\rho \dfrac{L}{A}$$ be unable to characterize the ...
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A question on the colours of the hydrogen spectrum

Why does hydrogen have 4 lines in the atomic spectroscopy and not more? I mean when an electron get excited it has more than 4 possible ways to return to the ground state. So why we see only 4 lines?...
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1answer
331 views

How to numerically solve the Schrodinger equation for the hydrogen atom?

From the analytical solution for the hydrogen atom I remember that the energies were obtained by boundary conditions and then the energy depends on n*n in which n is interpreted as different energy ...
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How to find many body states whose total $L_{z}$ eigen values are zero?

I am trying to solve construct matrix representation of Helium atom. The hamiltonian is , $$H=-\frac{1}{2}\sum_{i=1}^{2}\nabla^{2}_{i}-\sum_{i=1}^{2}\frac{2}{r_{i}}+\frac{2}{|\vec{r_{1}}-\vec{r_2}|}$$ ...
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146 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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171 views

Expected momentum of ground state hydrogen $<p>$

I am trying to calculate the expected momentum of an electron in the ground state of hydrogen atom. This is the wave function. So far I have done this:$$\iiint_V \Psi^* (-i\hbar) \frac {d\Psi} {dr} ...
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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 ...