# Tagged Questions

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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 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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### Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
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### Can scientists tell the energy levels of the atom?

In the hydrogen spectral series how did the scientists know the number of the energy level which the electron is moving from or to?
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### What happens when we bring an electron and a proton together?

I have a couple of conceptual questions that I have always been asking myself. Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each ...
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### Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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### Quantum mechanics and atomic bonding

I'm learning quantum mechanics in high school this year, and I have several doubts. I've done my research on various websites but my understanding is still fuzzy. I understand that when I punch a wall ...
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### Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
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### Aufbau principle in modern quantum theory

What is the rigorous definition of the Aufbau principle and the mathematical model used for its description? From Wikipedia, we have that the principle postulates a hypothetical process in which an ...
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### Effective Spin Interaction in Helium

My question is: what is the point of forming an effective spin-spin interaction for the exchange term in the variational analysis of Helium? Is there any significance to this term other than on ...
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### Electrons skip randomly around their orbits

I read where the electron (as well as a few other particles) skips around in its orbit randomly rather than move around the orbit smoothly. This effect has been repeatedly observed in the laboratory ...
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### Electron speed in Atoms

Is the speed of electrons in Atoms consistent in all Atoms or clusters/groups/individual elements, and if it is consistent in any atom, is that speed constant?
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### Questions on electron orbits

I have three questions to ask: Why do electrons (in an atom) specifically move in orbits and not some other type of motion? Where does the energy comes from, for the electron to move at much higher ...
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### Difficult to visualize Franck-Condon overlap

The franc condon principle says about the vertical transitions, means the coordinates of the nuclei remains unchanged during an electronic transition. But, what is the physical meaning or how to ...
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### spread of fock state distribution and infinite revival time of rabi oscillation in spontaneous emission

In cavity QED for a 2-level atom, the revival time for oscillation b/w the states $\left|\ e\ 0\right\rangle$ and $\left|\ g\ 1\right\rangle$ (absorbing the same photon that is emitted) is said to be ...
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### Electrostatic potential of a proton

I have been working on a quantum mechanical problem regarding the ground state of the Hydrogen atom. It appears that the best way to solve the underlying problem is to modify the electrostatic ...
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### What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
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### How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
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### Geometric quantization in Kepler problem in hydrogen atom

Why in the usual geometric quantization calculation the dimensions of eigenspaces is wrong (we can see this obstacle for Kepler problem in hydrogen atom). Here is a refference see
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### What is the reason for the electrons in a given subshell to orient in certain preferred regions?

My text book says: "Magnetic quantum number describes the behavior of electron in a magnetic field. We know that the movement of electrical charge is always associated with magnetic field. Since ...
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### What's an atomic superstate/superposition, and how is it possible?

What's an atomic superstate/superposition, and how is it possible? I understand the basics - being something can be moving and staying still at the same time; the observer changes the behaviour - but ...
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### Angular momentum of hydrogen from $n,l,m$ values

Given a wavefunction for hydrogen $\psi(n,l,m)$ it is possible to calculate its associated energy from $E=-13.6/n^2$. Does a similar equation exist for $L^2$ and $L_z$? That is, if we are given the ...
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### Is it that electron of an atom can be found anywhere in the space?

Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot, ...
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### Electron Decay, Why are there P and higher orbitals?

Related: Decay from excited state to ground state My confusion arose initially from the definition of binding energy being the lowest energy state (n=1) in the hydrogen atom. This, I assume, is ...
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### Do electrons collapse into nucleus, if electrons in the atom are constantly excited?

From the Bohr's atomic model, it is clear that electron can have only certain definite energy levels. When the electron is present as close to the nucleus as possible, the atom has the minimum ...
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### Why do electrons couple in atoms?

In describing electron states in hydrogen, we have a very "simple" picture, at least in intro-quantum. But this only has one electron! As we permit more electrons, we also have things like the ...
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### Why is the Bohr's idea of defined circular orbits overruled?

If we consider a thought experiment for determining position of an electron by using photons of light. According to principles of optics, if we use light of wavelength $\lambda$, then the position of ...
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### Gravitational Stark Effect

Could gravity induce line splittings in the optical spectrum of a molecule similar to the Stark or Zeeman Effects? Naively, a gravitational potential would be a simple addition to the Hamiltonian ...
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### What prevents an atom's electrons from “collapsing” onto its protons? [duplicate]

Forgive me if the answer to this is obvious. I have no formal physics training, and I remember that when I asked my physics teacher this, she just frowned and said "Good question." An electron is ...
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### Possibility of stable muonic structures?

In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it ...
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### Probability of absorption and emission of photons

Suppose you have a single electron in a box, and you shoot a single photon at it. How does one calculate the probability that the photon will be absorbed and the particle excited? Or that the photon ...
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### Does an electron move from one excitation state to another, or jump?

I'm wondering, when an electron changes state, does it move from one state to another over some (very small) time period? Or does it change from one state to another in no time? If the former, what ...
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### Aren't all electrons the same? So what about electron that absorbs photon?

I learned that electron absorbs a photon and goes into higher energy state. But also all electrons are identical. What is a difference between the electron in low orbital energy state? and the high ...
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### Why won't protons revolve around the nucleus containing electrons and neutrons?

In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets. Heavier the body,greater will be the ...
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### Density matrix and irreducible tensor operators

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information ...
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### Why is it energetically favourable for molecular bonds to form from a QM point of view?

For example, if you have two hydrogen atoms and an oxygen atom, they are all electrically neutral and don't attract each other. But then if they manage to get "close enough" somehow they snap together ...
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### Stern-Gerlach and Hund's second rule

According to Hund's second rule, the spin tends to be maximal. That would, in my understanding, imply that, regarding the Stern-Gerlach experiment, the important electron in a silver atom has spin ...
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### Quantum Mechanical Meaning of Atomic Orbitals

According to quantum mechanics, for multi-electron atoms, a single electron around the nuclei can be in the state of linear combination of different eigen energy states. In that case, even the energy ...
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### 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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### A Simple Explanation for the Schrödinger Equation and Model of Atom? [closed]

I tried reading the Wikipedia article to no avail - I simply cannot understand the Schrödinger Equation (what does each of the variables mean, especially the wave function), and the Schrödinger Model ...
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### 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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### Some questions regarding the behaviour of electrons [closed]

If I understand correctly: An atom acts a potential well for the electrons -- and particles in a potential well have discrete energy levels. There is a non-zero minimum to this energy called the ...
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### How to calculate the binding energy of electron of hydrogen atom by using uncertainty principle? [duplicate]

How to calculate the binding energy of an electron of hydrogen atom using uncertainty principle?
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### Why are the classical electron radius, the Bohr radius and the Compton wavelength of an electron related to each other?

Using the definition of the fine-structure constant $\alpha = \frac{4 \pi \epsilon_0 \hbar c}{e^2}$ and the Compton wavelength of an electron $\lambda_c = \frac{h}{m_e c}$ the classical electron ...
For example: $Xe^{+}+e^{-} \rightarrow Xe + \mbox{energy}$ Assuming that the electron has a kinetic energy $\neq 0$. Is the released energy a photon or heat?