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 ...

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Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
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1answer
1k views

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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1answer
1k views

Writing a Wavefunction as a Linear Combination of Eigenstates

We have the following wavefunction for the hydrogen atom: $$\psi(r,\theta,\phi)=\frac{1}{\sqrt{4\pi}}\frac{1}{(2a)^{3/2}}\frac{r}{a}e^{-r/2a}\sin(\theta)\sin(\phi)$$ where $a$ is the Bohr radius. ...
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1answer
111 views

Lifetime of 3d state shorter than 3s state in hydrogen atom

Can you say that the lifetime of the 3d state in the hydrogen atom is shorter than the one of the 3s state because the centrifugal energy associated with 3d is higher than the one associated with 3s? ...
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1answer
781 views

Reduced mass in quantum physics (Hydrogen Atom)

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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1answer
88 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
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1answer
72 views

What Elements Is Mono-atomic Hydrogen Capable Of Penetrating?

I recently learned that monoatomic hydrogen passes directly through solid aluminum and even combines inside aluminum to form $H_2$ which cannot pass through solid aluminum and therefore causes ...
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2answers
445 views

How does one calculate where the “surface” of a gas-giant would be?

Okay, so Jupiter, Saturn, et. al are gas giants. I understand that they have large gassy atmospheres, which, due to the pressure would eventually become more and more dense as one approaches the ...
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1answer
302 views

Volume charge density of H-atom

I have a problem where I am supposed to calculate the volume charge density of a neutral hydrogen atom. The potential is given to be $$ \Phi = k \frac{e^{-ar}}{r} \left(1 + \frac{ar}{2}\right) $$ Now ...
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1answer
503 views

Hydrogen ground state energy calculation?

We want to find the energy of a hydrogen atom ($Z=1$) in the ground state $$ \psi_{100} = \frac{1}{\sqrt{\pi}}e^{-r}\ \ \ \ \ \ (\mbox{atomic units}) $$ with Hamiltonian $$ H = ...
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2answers
168 views

Transition integral from 1-D cartesian into 3-D polar coordinate system

Lets say we have an electron which can be in two states. Its wavefunction for two states is then $\Psi=A\Psi_n + B\Psi_m$, where $\Psi$ is time dependent wave function. I know that the transition ...
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2answers
2k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
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1answer
268 views

Orbital of Hydrogen molecule

does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an ...
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2answers
112 views

Hydrogen cloud at the universe's beginning?

What prevented all of the hydrogen at the universe's start from coalescing into one gigantic star?
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73 views

Photon propagation direction prediction possible after interacting with neutral hydrogen?

My current line of research deals a lot with hydrogen's Lyman-alpha emission and subsequent interactions of the Lyman-alpha photons with the surrounding hydrogen gas. My question is whether ...
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1answer
258 views

How to determine the region that would contain a quantum particle

(a) A hydrogen atom is in its ground state. If space is divided into identical infinitesimal cubes, in which cube is the electron most likely to be found? If instead space is divided into 31 ...
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1answer
668 views

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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2answers
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Where does the Pauli Repulsive Force come from that counteracts the attraction between atoms and ions? [duplicate]

I'm learning about such things as ionic and covalent bonds, and the reason given for the ionic bonds is electrostatic attraction. However, if that were true, then the two ions would accelerate toward ...
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1answer
633 views

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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0answers
110 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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1answer
2k views

Stark Effect on the 1st excited state of Hydrogen

I know the ground state of hydrogen is unaffected by the Stark effect to first order. And I also know that the 1st excited state is split from 4 degenerate states to 2 distinct, and 1 degenerate state ...
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1answer
1k views

Hydrogen wave function in momentum space

We can seperate the wave function of an hydrogen atom in a radial and an angle part: $$ \phi_{n,l,m} (\mathbf{r}) = R_{n,l,m}(r) Y_{l,m}(\vartheta,\varphi) \, , $$ where $Y_{l,m}$ are the spherical ...
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1answer
896 views

Difference between atom and elementary particle questioned

Hydrogen ion doesn't have one electron which clearly mean that it has only one proton..So hydrogen ion is only a proton. Am I right, please make it clear. If hydrogen ion and proton are same that how ...
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1answer
921 views

Finding the wavelength of an electron in its ground state?

To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following? Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$ Solve for $p$ Use ...
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1answer
334 views

Ground state energy of hydrogen molecule ion

In this paper, it is mentioned: Furthermore, since the energy of $H_2^+$in the ground state must be lower than that of an H atom in the ground state,the negative (attractive) forces in the ...
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0answers
113 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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2answers
349 views

Why the hydrogen radial wave function is real?

Why the hydrogen radial wave function is real? Is it a coincidence?
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3answers
523 views

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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2answers
507 views

Technical detail in the solution of the hydrogen atom

I'm trying to do an exercise in which you solve the Schrödinger equation for the hydrogen atom. Through the exercise, I've already shown that the wavefunction is: $$ \psi_{n\ell m}(r,\theta,\varphi) ...
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2answers
390 views

Hydrogen atom in quantum mechanics

I have problems following the calculations in Griffiths' Introduction to Quantum Mechanics (Chapter 4.2.1): If you apply the Schrödinger equation to the Coulomb potential you get the following ...
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0answers
124 views

Geometric quantization of a hydrogen atom

I want to know how to quantize a hydrogen atom as an example of geometric quantization. Apparently there is a derivation in the book "Geometric Quantization in Action: Applications of Harmonic ...
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2answers
609 views

What's the difference between two Hydrogen atoms?

If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location ...
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2answers
454 views

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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Wave function of Hydrogen Atom [closed]

Wavefunction of a Hydrogen atom is expressed in eigenfunctions as: $$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$ Is ...
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3answers
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Expectation values of $(x,y,z)$ in the $|n\ell m\rangle$ state of hydrogen?

Expectation values of $(x,y,z)$ in the $| n\ell m\rangle$ state of hydrogen? Does anyone know of a quick way of finding this (if there is even one)? Can I somehow use the relation that: $$\langle ...
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2answers
2k views

Why is the binding energy per nucleon not zero for hydrogen atom?

The lone proton has not to be worked on against any electrostatic force. So where does the energy come from? What is mass defect for a hydrogen nucleus?
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2answers
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Jupiter Core is Solid Hydrogen

I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an ...
2
votes
1answer
668 views

Theoretical treatment of Hydrogen bond?

I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from ...
2
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1answer
159 views

Hydrogen Hyperfine Structure: General Expression

I was looking at the hyperfine structure for the hydrogen atom. I checked pretty much every textbook I knew but none of them gave me the general expression for the energy correction due to the ...
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1answer
158 views

can hydrogen stay frozen in vacuum?

I've look into the hydrogen state diagram, and it seems that it can be frozen under pressure. Question: Does this mean that hydrogen cannot be kept frozen in a vacuum chamber?
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340 views

Water, can it break through temperature?

If water is heaten up to ridicilously high temperatures, is it possible for the atoms in the molecules to lose their bonds? And if it is possible, isn't this some kind of chain-reaction? Like you ...
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2answers
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magnetic moment of proton

I just tried to calculate the magnetic moment of a proton. I took the proton g-Factor of $g=5.585694$ nuclear magneton of $\mu_k = 5.050783 * 10^{−27}$ J/T proton spin of $I=1/2$ At first I ...
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0answers
820 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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1answer
164 views

Can atmospheric hydrogen be collected for use?

Just what the title states. Free hydrogen accumulates in the exosphere. At high altitudes there are large volumes of open space between molecules - which would be a hindrance to collection. Would ...
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1answer
87 views

Spectrum measurement

How can be spectrum of hydrogen measured (Lyman series, Balmer series, Paschen series and so on)? I mean schema of measurement circuit and the measuring technique (including all the steps needed). Is ...
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5answers
1k views

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 ...
2
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1answer
289 views

Electric dipole transitions/expectation value of position

Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have $$ \int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0 $$ for the position vector $\vec{r}$. (This is for ...
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4answers
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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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4answers
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why ammonia is not a competitive energy carrier?

reading this article about Germany planning to store renewable energy as hydrogen gas, i'm left wondering why they deem so great this plan, compared with other alternatives like ammonia as a energy ...
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0answers
551 views

Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]

I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks! Consider the Hydrogen Atom Hamiltonian: $$ H = (\mathbf p^2/2 ...