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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Solving Schrodinger equation for the hydrogen atom

In University Physics with Modern Physics by Hugh Freedman in Chapter 41.3 they go about solving the Schrodinger equation for the hydrogen atom. At one step they say to substitute the following ...
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E-k diagram of hydrogen atom

The energy of a free (nearly free) electron in a solid (say, metals) is given by $E=h^2k^2/2m$ where k is the momentum vector, h is Planck's constant and m is the mass of the electron. This ...
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What happens to a hydrogen atom under an intense gravitational field (or intense acceleration)?

I'm curious how the observed quantum-mechanical properties of a hydrogen atom would change under very high gravitational fields. Do the energy levels change? Do the chemical bonding properties ...
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Why is hydrogen-boron called a fusion reaction?

As we know, we usually call fusion such a reaction in which two light nuclei make a heavier one and release energy. For fission, a heavy nucleus breaks into light ones. My question is, in proton-boron ...
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How to get Bohr model from Schroedinger equation? [duplicate]

New theories must in some approximation must reduce to older approximately correct theories. In what approximation exactly does the angular momentum quantization condition from Schroedinger's equation ...
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Is the radiation problem actually solved in the classical quantum model of hydrogen?

It's often said that in classical physics a electron-proton system is not stable due to "Bremsstrahlung" and that one instead has to look at it quantum mechanically. This doesn't make sense ...
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What do maufacturers do to ensure that a valve is capable of containing hydrogen gas? [closed]

I am a researcher working to develop a hydrogen fuel system for use in a specialized internal combustion engine. The biggest challenge from an engineering standpoint with a project such as this is the ...
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Forces during the formation of hydrogen molecules

In my book it is given that for the formation of hydrogen molecules, hydrogen atoms come closer due to net attractive forces. It is written that initially when the atoms were approaching towards each ...
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Hydrogen Atom in Second Quantization and Two-Particle Bases

Context: In non-relativistic QM and many-body theory, the second quantization formalism allows us to write a Hamiltonian for a many-body system with up to two-body terms as (up to a re-ordering ...
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Is $e^-$ in 1st excited state in the $\rm H$-atom in superposition of possible ($l,m,s$ for $n=2$) substates/in superposition of all possible states?

I want to know how we can determine the probability of various states of hydrogen as there are infinite of them, or electron in a hydrogen atom is in the superposition of which states, maybe it is in ...
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Question about the radial hydrogen eigenfunctions

When calculating the selection rules for electronic transition in the hydrogen atom in dipole approximation, we always focus on the angular integrals. But why the integral $$ \int_{0}^{\infty}[rR_{nl}(...
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Origin of $\ell \leq n-1$ orbital rule

I am wondering about the origin of the $\ell \leq n-1$ orbital filling rule. For the hydrogen atom, I believe the reason is because in the spatial wave function there is the term $$\psi \propto \sqrt{(...
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Hydrogen Emission vs Absorption Wavenumbers

I am used to using the formula $ R_H (\frac{1}{n^2_{final}}-\frac{1}{n^2_{initial}}) $ to calculate the transition wavenumbers when an electron in a Hydrogen atom emits a photon. Can you use the same ...
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Schrödinger's equation for hydrogen atom (azimuthal part) [duplicate]

Now, The azimuthal part of the Schrödinger's equation for a hydrogen atom (after separating variables) is: $$ \frac{d^2 \Phi}{d \phi^2} + m^2 \Phi = 0$$ Which has solution $A e^{im\phi} + B e^{-im\phi}...
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How to calculate radius of the $n$th Bohr orbit if the nucleus is not at rest relative to the center of mass?

I've been dealing with a couple of questions regarding Bohr's model except where the mass of the nucleus is not negligible compared to the mass of the (revolving) electron. According to my book (...
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Transition $2p \rightarrow 1s$ of Hydrogen Atom

I am reading Mukhanov and Winitzki's book Introduction to Quantum Effects in Gravity and in second paragraph of Sec. 1.4.2 they say that : The spontaneous emission by a hydrogen atom is the transition ...
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Nodes in Spherical Harmonics

In Rydberg Atoms book by Thomas F. Gallagher, Page 14, the author provides the general equation of spherical harmonics which is well-known. He states that there exist $l-m$ nodes in the $\theta$ ...
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Schrodinger Equation of a Hydrogen Atom in a Rydberg State

I am not a mathematician, so I really appreciate it if someone could explain it in a simple way. In Rydberg Atoms book by Thomas F. Gallagher, the Schroedinger equation for the H atom in atomic units ...
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Are there any special websites or data files for materials like tritium?

I was looking for tritium cost per gram online, but i didn't find anything that can be taken as a reference for a scientific article. Wikipedia mentioned its costing of 2000, but i need more recent ...
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Wave Function Collapse During Reactions

When a proton and electron combine to form Hydrogen gas after the big bang, would the wave function of the electron collapse as they bond together?
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Position and momentum of an electron in a hydrogen atom [closed]

What can be expected as results for a set of position and momentum measurements of an electron in a hydrogen atom? I believe that for the position, we can expect something depending on the radial ...
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QED and Hydrogen atom mass

Hydrogen Atom as a bound state in QED(Assuming Proton as an elementary particle) has a certain mass that as far as I remember, we're taught in High School its mass is the sum of the mass of its ...
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Why do we normalize the radial and the angular parts of a spherical wavefunction separately?

I'm trying to revise the Quantum Mechanical model of the Hydrogen atom, and I understand all the methods involved, including separating the wavefunction into its radial and angular parts, solving all ...
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Hydrogen atom at $T=0K$ [closed]

If I have an hydrogen atom at $T=0K$ from Boltzmann distribution I can have only the G.S populated, so if I send to this atom photons at all energies is impossible to excite the atom, is this right? ...
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Why do we ignore the proton when computing relativistic correction in the Hydrogen atom?

I have read a number of textbooks (e.g. Sakurai), and they all seem to say that the unperturbed Hamiltonian of hydrogen is: $$ H_0 = \frac{p^2 }{2m_e} - \frac{e^2}{r} \tag{1} $$ and the relativistic ...
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Associated laguerre polynomials for the hydrogen atom

The associated laguerre polynomial $L_k^N$ is a solution to the differential equation: $$ xy'' + (N + 1 - x)y' + ky = 0 $$ For the reduced radial equation for the hydrogen atom, we know that the ...
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Time-Depedent Pertubation Theory - Ionization Rate of a Hydrogen Atom

So, i was studying Time-Depedent Pertubation Theory, using the book "Lectures on Quantum Mechanics" by Steven Weinberg when i ran across this problem: "Calculate the rate of ionization ...
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Is the Bohr radius deprecated?

The Bohr radius ($a_0$ or $r_{\text{Bohr}}$) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after ...
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Expectation value of $r$ [closed]

I am looking for an analytical expression for $$\langle r\rangle = \int dr r^2 R_{n'l'} r R_{nl}$$ where $R_{nl}$ are the radial wave functions, defined as $$R_{nl}(r)=N_{{nl}}\,r^{{l}}\,e^{{-{\frac {...
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Magnetic moment of an electron in a hydrogen-like atom

My textbook offers a derivation of the magnetic moment of an electron in a hydrogen-like atom starting from the pronebility current density. I'll offer a brief description of the work. Firstly, we ...
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Hydrogen atom and scale transformation for radial variable

While solving Schrödinger equation for Hydrogen atom we make a scale transformation for radial variable ($r=\frac{ax}{Z}$; where $a=$ Bohr radius, $x=$ dimensionless variable and $Z=$ atomic number), ...
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What effects broaden the discrete hydrogen atom? (Validity of the application of Fermis golden rule to dipole radiation)

I'm not asking for any of the relativistic corrections to the hydrogen atom. These only cause splitting of the discrete spectrum in a slightly different discrete spectrum. I'm asking for effects which ...
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Is there a quick yet semi rigorous way to derive the Bohr radius of hydrogen?

I will be taking an oral exam, where I have to do some "airport physics", fast and easy magnitude estimations. Currently I try to come up with a good way to find the Bohr radius of the hydrogen atom ...
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Interpretation of probability current density of hydrogen atom wave function

I'm trying to understand the physical interpretation of the value of the probability current density of an electron in a hydrogen atom: $$j_r=0$$$$j_{\theta}=0$$ $$j_{\phi}=\frac{h}{rsin\theta}|\psi_{...
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Question about perturbation theory and even and odd wavefunctions

I was solving a question about perturbation theory and I came across something my teacher didn't mention and I can't seem to understand it. In the question there is an external electric field on a H-...
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wavelengths of all emission spectral lines of the hydrogen atom which was excited to the state with the principal quantum number $n= 3$

Calculate the wavelengths of all possible emission spectral lines of the hydrogen atom which was excited to the state with the principal quantum number $n= 3$. Is this just a case of applying the ...
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Localizing position of electron in hydrogen atom

Consider the hydrogen atom, just taking into account the electrostatic force and not magnetism nor spin. Is it possible to take the wave functions of the energy eigenstates of that hydrogen atom, ...
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How can heavier elements be made from hydrogen atoms?

In a JRE podcast from a few years ago, talking about the idea of a universal constructor, Sam Harris said that we could go to a near-vacuum area of deep space, collect nothing but hydrogen atoms, ...
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Do the hydrogen atom's electron orbitals have Gaussian probability density functions?

In this article they show the following diagram: Are all the diagrams in the little boxes really just Gaussian probability density functions with mean and variance (or covariance)? If not, what kind ...
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How to get effective quantum numbers of a linear combination of $\rm H$-atom wavefunctions?

The convention for the Hydrogen atom's interpretation subject to the laws of quantum mechanics is that you can prove the quantization of $|L|$, $L_z$, and Energy through quantum numbers $\ell$, $m_\...
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In what sense are boron and carbon the simplest examples of degenerate atomic ground states?

According to this accepted answer, the most simple example of two atoms with degenerate ground states are boron and carbon. But hydrogen is the simplest of all which has the ground state configuration ...
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Two dimensional hydrogen atom

I was trying to solve for the wave function of an electron in a hydrogen atom confined to only two dimensions (in flatland). First of all I figured out the electrostatic potential energy in flatland. ...
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Complex energy interpretation in perturbation theory

I'm working on time-independent degenerate perturbation theory for the Hydrogen first excited state. I have the following perturbation $H$: $H = \lambda V_0 \sin^2 \theta \sin 2\phi = \lambda V$. We ...
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Frequency of photons emitted by hydrogen atoms

I'm learning about quantum physics, and I'm afraid I'm barking up the wrong tree when attempting to solve questions. Can anyone please have a look and see if this is the right way to solve this? Q1:...
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Ground state of hydrogen molecule using Heitler–London method (H-L)

I am reading The Theory of Magnetism I, by Mattis. In Chapter 2, a hydrogen molecule is studied in the following way: We have a Hamiltonian of a hydrogen molecule: $$H = H^0_1 + H^0_2 + H^\lambda \...
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Why must energy transitions in hydrogen atom be between stationary states?

In Griffiths QM textbook, he said that a hydrogen atom in the ground state may undergo a transition to some other stationary state by absorbing a photon. Why must this transition be to another ...
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Peak function decision

I am doing a lab of locating hydrogen's spectral lines and peak function fitting is required. It is suggested to use Lorentzian to locate the peaks. I wonder why don't we use Gaussian instead?
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Does the proportion of strong nuclear force in a star change during nuclear fusion?

I read that the SNF accounts for 99.9% of the mass of an atom. So if 4 hydrogen atoms become 1 helium atom during nuclear fusion does that change the proportion of SNF as we have 4 SNFs becoming 1 ...
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What causes a double peak for a single wavelength when using an optical spectrometer system?

I am doing an experiment to determine the Rydberg constant for the Balmer series using an optical spectrometer system (consisting of a monochromator with a photomultiplier detector and pulse counting ...
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Guessing eigenvalue solution

I am reading The Theory of Magnetism I, by Mattis. In Chapter 2, he proposes the following eigenproblem: $$ \left ( \begin{matrix} V & U \\ U^\dagger& V \end{matrix} \right ) \left ( \begin{...

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