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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Why are hydrogen energy levels degenerate in $\ell$ and $m$?

Is there a good physical picture of why the energy levels in a hydrogen atom are independent of the angular momentum quantum number $\ell$ and $m$?
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Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
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How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
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Why are the higher angular momentum states of a hydrogen atom closer to the nucleus?

I was looking at a plot of hydrogen radial wave functions $r^2|R_{nl}(r)|^2$, and I noticed that for fixed $n$, the states with smaller $l$ were "further out" from the nucleus. This conflicted with ...
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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 ...
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Proton - neutron fusion?

In reviewing some problems in an elementary book, I ran across a reference to the reaction $p+n\rightarrow d$ + "energy". Is that possible? I don't see any reason why not, but I don't find any ...
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Fusion: Why deuterium and tritium?

I would like to know why scientists try to use deuterium and tritium for fusion and not just the ordinary isotope of Hydrogen ${}^1H$?
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What are independent parameters in Hellmann–Feynman theorem?

A typical example in textbooks about the application of Hellmann–Feynman theorem is calculating $\left\langle\frac{1}{r^2}\right\rangle$ in hydrogen-like atoms. Wikipedia has a nice demonstration of ...
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Reduced mass in quantum physics (Hydrogen Atom) [duplicate]

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
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For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly?

My google news page has burst forth the news that metallic hydrogen has been produced in a laboratory using a diamond anvil cell. Only one service mentions (at this particular moment) that it has been ...
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What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ \left(-\frac{\hbar^2}{2\...
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What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
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Why are S-state solutions of Dirac equation for hydrogen atom allowed to be unbounded?

In this Wikipedia page there's a statement about 1S orbital as solved from Dirac equation: Note that $\gamma$ is a little less than $1$, so the top function is similar to an exponentially ...
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How big is an excited hydrogen atom?

Suppose an empty universe with the exception of a single hydrogen atom (1 proton, 1 electron). The electron may be in its ground state or it may be excited a certain number of levels. Suppose it is at ...
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How does the electron jump across “gaps” in its orbital?

I saw on perhaps COSMOS, and have heard mention from other professors, that electrons sort of "teleport" or something, in their orbital and the quantum level. So looking at the orbitals for a lone ...
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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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H atom's excited state lasts on average $10^{-8}$ secs, is there a time gap (of max 2*$10^{-8}$ secs) betwn. two consec. photon absorpt.-emiss. pairs?

OK here is a description of what happens: time=0,timer starts first absorption happens, first emission happens absorption #2 happens emission #2 happens, stop timer timer==? According what I found, ...
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How long will the Universe's hydrogen reserves last for?

I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions. Here ...
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What does ionization of neutral Hydrogen have to do with “transparency”?

Most accounts of the early history of the Universe make some reference to (re)ionization as being the reason that the Universe becomes transparent after a period of opacity caused by the absence of ...
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How would one detect antihydrogen in the universe?

Since the spectra of hydrogen and antihydrogen are the same, how do astronomers know which one they're detecting? Is, perhaps, the Lamb shift in antihydrogen different?
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Are there published predictions that hydrogen could remain metallic at ambient pressure?

Below the question For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly? there is a comment that directed me to the BBC News ...
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Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
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Have the Rowan University “hydrino” findings been replicated elsewhere?

In 2009, Rowan University released a paper claiming to replicate Blacklight Power's results on energy generation using hydrino states of the hydrogen atom. The paper (link now dead) appears to ...
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Why is hydrogen the most abundant element in the Universe?

Hydrogen is the most abundant element in nature. Does cosmological nucleosynthesis provide an explanation for why is this the case? Is the explanation quantitatively precise?
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Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' |...
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Can open, unsafe nuclear fusion reaction burn the atmosphere?

I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts. Nuclear fusion reaction requires $15*...
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Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
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$SO(4,2)$ symmetry of the hydrogen atom

The hydrogen atom with Hamiltonian obviously has $SO(3)$ symmetry since it just depends on the radius. $$ H = \frac{\mathbf{p}^2}{2m} - \frac{k}{r}$$ This is generated by angular momentum $\mathbf{L}...
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Hydrogen radial wave function infinity at $r=0$

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$ I understand that the radial ...
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Collision between electron and proton?

What would happen if an electron collided with a proton such that the two do not collapse? Would the two become a unit, or would some force prevent them from bonding thus forcing the electron to orbit ...
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Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar, \qquad n\in\...
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Is there any time-dependent hydrogen atom Schrödinger equation, solvable analytically?

It's well-known that hydrogen atom described by time-independent Schrödinger equation (neglecting any relativistic effects) is completely solvable analytically. But are any initial value problems for ...
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Size of positronium

Positronium consists of an electron and a positron. By what factor is a positronium atom bigger than a hydrogen atom? The solution has been explained to me. The characteristic length when solving for ...
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Calculating the most probable radius for an electron of a hydrogen atom in the ground state

This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state. It states that : The radial probability density for the hydrogen ...
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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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How is Bohr's model related to electron cloud models via the correspondence principle?

I came across a discussion of atomic Rydberg states, which appear to be defined as having their outer electron in a highly excited state. In the same text, it mentioned that these excited electrons ...
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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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Continuous spectrum of hydrogen atom

I wonder if there is a nice treatment of the continuous spectrum of hydrogen atom in the physics literature--showing how the spectrum decomposition looks and how to derive it.
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How does the hydrogen atom know which frequencies it can emit photons at?

At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the ...
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How can we describe the electrons of multi-electron atoms (i.e. not Hydrogen) when equations/analytic solutions only exist for Hydrogen?

I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the single electron in the ...
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How can one describe electron motion around hydrogen atom?

I remember from introductory Quantum Mechanics, that hydrogen atom is one of those systems that we can solve without too much ( embarrassing ) approximations. After a number of postulates, QM ...
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Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
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What is the difference between the Bohr model of the atom and Schrödinger's model?

What is the difference between the Bohr model of the atom and The solution of the Schrödinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
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Solution of 1-D Schrodinger equation for the potential $V(x) = -\frac{1}{|x|}$

May be this question might have already been asked but i couldn't find it, so let me know if its already there. Consider a potential, $V(x) = -\frac{1}{|x|}$ and if we apply this to a one dimensional ...
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Is there a list of hydrogenic transition matrix elements online?

Calculating transition matrix elements can be difficult, and I have found myself needing to use hydrogenic electric dipole transition matrix elements a fair bit. $$\mathbf{r}_{nlm}^{n'l'm'}=\langle\...
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Pure hydrogen star

What is the smallest mass of pure hydrogen that can ignite fusion? That is can population III stars have tiny masses? How would such stars develop? How long would such a star last?
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Hydrogen atom, what's the wave equation for the atom's nucleus?

I learned from the class about the equation for hydrogen atom's electron where textbook assumed that the center/nuclei of hydrogen atom was fixed at origin. However, since every particle was a wave, ...
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Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
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Bessel vs. modified Bessel in radial equation of hydrogen

I am trying to understand the difference between Bessel functions and modified Bessel functions (simply googling is yielding complicated, non-intuitive answers). I was under the impression that one ...
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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 $\frak{A}$ ...