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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49 views

Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l ...
3
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1answer
352 views

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 ...
0
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1answer
31 views

Z coordinate expectation value of the Hydrogen atom

I want to find $z-coordinate$ expectation value $\textbf{<z>}$ of the Hydrogen atom wave function $\psi_{1,0,0} = (\pi a^3_0)^{-1/2}e^{-r/a_0}$ in its ground state. I read in some text that ...
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0answers
6 views

Why does concentrated parahydrogen in hydrogenation reaction exhibit hyperpolarized signals in proton NMR spectra?

In wikipedia it says "When an excess of parahydrogen is used during hydrogenation reactions (instead of the normal mixture of orthohydrogen to parahydrogen of 3:1), the resultant product exhibits ...
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1answer
35 views

Water + RF + Spark = Continuous Fire

Can anyone explain the physics of what is happening in the following video? https://youtu.be/p8xYUDiSGDk?t=37 Is this process Radiolysis? At what radio frequency & power level is h20 ...
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2answers
23k views

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 ...
0
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0answers
14 views

How is the Lyman alpha forest and Gunn-Peterson trough evidence for Reionization? [duplicate]

I'm trying to understand how the Lyman alpha forest and Gunn-Peterson trough are evidence for Reionization. From what I've read, the Lyman alpha forest tells us how much neutral hydrogen is in the ...
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1answer
55 views

Deriving the Bohr radius of a hydrogen atom using Schrödinger's equation

I'm trying to follow the book for the introduction to quantum mechanics by Griffiths. I'm following the part where he is solving Schrödinger's equation for the hydrogen atom. There, he found the Bohr ...
2
votes
2answers
898 views

Is a free proton a positive Hydrogen-1 ion?

The Hydrogen-1 isotope is a form of hydrogen with 1 electron, 1 proton, and 0 neutrons. If that isotope were to lose its electron (thus being a Hydrogen-1 ion with a positive charge) what would be ...
2
votes
2answers
101 views

Temperature of fusion in the Sun vs. fusion in controlled experiments on Earth

I recently learned that hydrogen fusion (i.e., hydrogen to helium) experiments on Earth have been successful at temperatures in excess of 100,000,000 degrees Celsius. However, I also learned that ...
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3answers
61 views
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2answers
501 views

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 ...
1
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1answer
52 views

Fusing Hydrogen with lightning

I've been reading about fusion recently (Specifically Deuterium fusion) and a friend of mine asked me if it was possible to fuse two Deuterium atoms with a lightning strike? Now this question has a ...
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1answer
43 views

How does speed of gas molecules change with pressure? [closed]

A thought experiment. I have a box of fixed dimensions, inside this box I have molecules of $H_2$ at constant temperature. I'll be gradually increasing pressure inside the box and the temperature ...
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1answer
41 views

Does the proton wobble due to the electron's orbit in a Hydrogen atom?

In a hydrogen atom the nucleus only has one proton and no neutrons so the electron to nucleus radio is higher for hydrogen than that for any other atom. Does the orbiting electron induce a wobble on ...
2
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0answers
41 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) = ...
4
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3answers
603 views

Using the uncertainty principle to estimate the ground state energy of hydrogen

I have been reading through this estimate of the ground state energy of hydrogen and others like it. In this one it says it is using the uncertainty principal but then proceeded to use the following: ...
1
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1answer
44 views

The point of charge neutrality in the Hydrogen Atom

If we treat the Hydrogen Atom like the Bohr model then we have a proton in the center with an electron orbiting at some radius (the Bohr radius). In this picture you can imagine the electric field ...
6
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2answers
355 views

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 ...
2
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2answers
127 views

In the hydrogen atom, why is the electron orbital spherical rather than flat like a 2D orbit plane?

In a hydrogen atom an electron is orbiting around a proton, similarly to a moon around a planet. The orbit of a moon around a planet is flat (2D) whereas the orbit of an electron around a proton is ...
3
votes
2answers
70 views

Why is the blue line in the Balmer series sometimes not visible?

So I've conducted an experiment to find the four visible hydrogen emission spectrum lines in the Balmer series in a laboratory. I don't have any background in quantum physics. When I looked through ...
0
votes
3answers
87 views

Quick way to compute $\langle n^{'}l^{'}m^{'}|r^k|nlm \rangle$, $k \in I$; $|nlm\rangle$ is $H$ atom eigenfunction [closed]

I want to compute quickly (using maybe some scaling arguments) $\langle n^{'}l^{'}m^{'}|r^k|nlm\rangle$, where $k \in I$. $|nlm \rangle$ is the eigenfunction of the Hydrogen atom ($H$). Example: ...
0
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1answer
65 views

Confused on how to interpret the energy eigenfunction of Hydrogen

So here is an image of the third lowest energy eigenfunction of an electron in a hydrogen atom: Image from http://imgur.com/Lu4MocL I understand well the eigenfunctions given by Schrodinger's ...
0
votes
1answer
19 views

Hyperfine lifetime calculation: what is the spin eigenfunctions?

I'm trying to calculate the lifetime of the 21 cm line in hydrogen and have the following expression: $\frac{1}{\tau} = \frac{4\alpha}{3}\omega_{if}^3|\langle a_f|\vec{x}|a_i\rangle|^2$. The ...
0
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1answer
20 views

Temperature moderation

Temperature moderation is closely related to the hydrogen bond, as you guys all know. And this temperature moderation happens everyday to human beings through perspiration. As the water in you body ...
3
votes
1answer
210 views

Algebraic solution of Dirac equation for Coulomb potential

The Runge-Lenz operator enables an algebraic solution of Coulomb potential energy levels without a solution of a differential equation. What is the analog for the solution of the Dirac equation in a ...
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3answers
1k views

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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4answers
2k views

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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2answers
209 views

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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2answers
53 views

What is the relation between energy levels of hydrogen atom in Bohr's solution to that of Dirac solution

In Dirac solution for hydrogen atom, the energy levels are calculated as positive \begin{equation} ...
0
votes
1answer
76 views

I don't understand the spectrum of elements e.g. hydrogen spectrum [closed]

Quote from my textbook The hydrogen spectrum has spectral lines which correspond to transitions of the electron between energy levels. This statement implies that hydrogen has multiple electron ...
0
votes
1answer
82 views

How can you use the Delta Function to find the Electric field inside of a Hydrogen Atom?

This is a problem from my homework, but I'm lost conceptually on how to do it. I'm not looking for someone to do the work for me, I'm looking for some guidance on how I can set it up/understand it ...
4
votes
2answers
432 views

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 ...
0
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1answer
66 views

Two-body systems quantum physics (Transformation) [closed]

Given the Schrödinger equation $i\hbar \frac{\partial}{\partial t}\Psi(\vec r_1,\vec r_2,t) =\left [ -\frac{\hbar^2}{2m_1}\nabla_{r_1}^2-\frac{\hbar^2}{2m_2}\nabla_{r_2}^2 +V(\vec r_1,\vec r_2)\right ...
5
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1answer
1k 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 ...
2
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2answers
105 views

Schrödinger eq. for H-Atom

The stationary Schrödinger equation for the hydrogen atom is given by $ \left(-\frac{\hbar^2}{2m_e}\Delta_e -\frac{\hbar^2}{2m_k}\Delta_k - \frac{Z e^2}{4\pi \varepsilon_0 |\vec r_e - \vec r_k|} ...
4
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1answer
157 views

Why is metallic hydrogen degenerate matter?

Why is metallic hydrogen considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force ...
4
votes
3answers
626 views

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 ...
0
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1answer
78 views

Transition of H to hydrino H(1/4) by HOH as the catalyst

Is this real, is there a more stable form of Hydrogen atom? Source : Mechanism of Soft X-ray Continuum Radiation from Low-Energy Pinch Discharges of Hydrogen and Ultra-low Field Ignition of Solid ...
4
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1answer
118 views

Can hydrogen be used for superconductors?

I learned that heaver isotopes of a substance have a lower superconductivity transition temperature. Does this mean that things like hydrogen which are lighter can be used for high temperature ...
0
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1answer
53 views

Show that the minimum energy value for a given $l$ increases as $l$ increases

"Consider a particle in a central field and assume that the system has a discrete spectrum. Each orbital quantum number $l$ has a minimum energy value. Show that this minimum value increases as $l$ ...
0
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2answers
71 views

Using slope=0 technique to find most likely spherical shell

In this PDF http://riedo.gatech.edu/Teaching/Modern_Physics/hw/HW3_2010_MP_SOL.pdf problem#1, the instructor solves the question of which spherical shell (what radius $r$) has the greatest ...
0
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0answers
55 views

Is this solvable? Time-dependent perturbation theory

The question is A hydrogen atom is placed in a time-dependent homogeneous electric field given by $$ \varepsilon(t) = \varepsilon_0(t^2 + \tau^2)^{-1} $$ where $\varepsilon_0$ and ...
2
votes
4answers
3k views

What makes water heavier than air?

I apologize in advance if this is too basic for this site. Considering that hydrogen is lighter then oxygen, and water is 2/3 hydrogen, and only 1/3 oxygen, and our "air" is comprised mainly of ...
0
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1answer
53 views

Why is there no $1S_{-1/2} $ state of the hydrogen atom?

Heyho, i found this term scheme for the hydrogen atom: https://upload.wikimedia.org/wikipedia/commons/9/94/Wasserstoff_Aufspaltung.svg I was wondering why there is only a $1S_\frac{1}{2}$ state and ...
4
votes
4answers
3k views

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 ...
1
vote
2answers
95 views

What causes the death of the Sun?

In a previous question I learned that in each second only a miniscule portion of the total hydrogen in the Sun is converted to helium and that the number is 1/10^18 of its mass converted each second. ...
0
votes
2answers
83 views

Where do atoms of H and He go when they rise in the atmosphere? [duplicate]

What happens to atoms/molecules of H and He when we let them freely fly in atmosphere do they get into space? Is there any particular way to enumerate the 'force' that drives them upwards? Does ...
0
votes
1answer
121 views

Where is the Hydrogen the Sun consumes?

I understand the Sun consumes 600,000,000 tons of Hydrogen each second. Where is this Hydrogen? Is all the Hydrogen the Sun will ever consume inside it or are there vast amounts of Hydrogen in space ...
0
votes
2answers
93 views

Changing coordinates in partial derivatives, re: Hydrogen atom

At around 11:35 in this video https://www.youtube.com/watch?v=q99ygFeWGv4 the instructor is using a "standard way of changing coordinates" in partial derivatives relating to the new variables of ...