All Questions
Tagged with wavefunction atomic-physics
83
questions
0
votes
1
answer
102
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Moments of hydrogen orbitals/Transition dipole moments
I'm interested in calculating transition dipole elements for atomic transitions. This means I would like to calculate things like
$$
r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle
$$
...
- 14.4k
-3
votes
1
answer
93
views
Could an electron wavefunction wrap multiple times around its orbit?
In the Bohr model a whole number of electron de Broglie waves with $\lambda=h/mv$ fit around an orbit with radius $r$ so that we have:
$$2\pi r=n\lambda.$$
But could the electron waves wrap around the ...
- 5,925
4
votes
5
answers
384
views
Why are electron orbitals shaped how they are?
I'm new to quantum physics, but as far as I've understood, electron orbitals are defined as the region where an electron has a 90% probability to be. Unless I'm wrong, every point has some probability ...
- 51
11
votes
1
answer
1k
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How is the proton accounted for in the relativistic solution of the hydrogen atom?
In the non-relativistic limit, the Schrodinger equation for the hydrogen atom can be solved using reduced mass techniques to account for the motion of both the electron and proton.
I am wondering if a ...
- 2,122
0
votes
1
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76
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Calculation of Einstein coefficient for spontaneous emission [closed]
I want to calculate the rate of spontaneous emission for the transition: $|3,2,2\rangle$ to $|2,1,1\rangle$ in a hydrogen atom.
Corresponding to the formula of $A_{ab}$ the only thing to derive is the ...
- 308
1
vote
2
answers
302
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Why is the antisymmetric wavefunction for a $\rm H_2$ ion higher in energy and why can no stable molecule be formed in this state?
I just want to make sure my basic understanding of this is correct.
When the internuclear distance is finite, the symmetric wavefunction of the electron is lower in energy because it experiences a ...
- 220
2
votes
2
answers
126
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From standing matter waves of the atoms to Schrodinger equation [closed]
I read in the Resnick - Halliday Physics textbook (2nd edition):
"The idea that stable states in atoms correspond to standing matter waves was adopted by Erwin Schrodinger in 1926 and used by ...
-1
votes
1
answer
60
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Interference of atomic orbitals: In what field do atomic orbitals oscillate? [closed]
I am learning molecular orbital theory for chemical applications. To understand why molecular orbitals can be antibonding, destructive interference aka out-of-phase interference of the orbital ...
- 121
3
votes
1
answer
129
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Can we think of spontaneous emission of a photon from an excited atom as a driven harmonic oscillator problem?
This is a kind of strange question, but I'm wondering, in the context of a fully quantum field theoretic treatment of spontaneous emission, if there is any model or way of calculating the process that ...
- 315
1
vote
0
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60
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Ground state of hydrogen atom, $e^{-\kappa r }$ or $e^{-\kappa r }/ r$
The ground state must be an $s$-wave state, so it depends only on the radius $r$. I cannot remember the exact form, but I know it must be one of the two.
Is there any simple way to determine which one ...
- 1,957
2
votes
1
answer
71
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How exactly does wavefunction of an electron change when it ceases being part of an atom?
This is a followup of How are electrons really moving in an atom?
As it happens, reading answers to that question I, instead of understanding more, lost some of my previous understanding.
Particularly,...
- 513
-1
votes
2
answers
140
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Different versions for the Radial Solution of the Hydrogen Atom [closed]
Initially, I'm trying to prove if the following is true
$$|\psi_{n00}(r=0)|^2 =\dfrac{1}{\pi n^3a_0^3}$$
I'm looking to solve some calculations made in
Introductory Quantum Optics
Christopher Gerry ...
- 3
3
votes
2
answers
463
views
How does $s$ subshell not have a node in the center despite the nucleus being there?
In most images of $1s$ subshell I see that there's no node shown at the center, and even the formula $n-\ell-1$ gives 0 as the answer.
But, isn't the nucleus experimentally proven to be at the center? ...
- 33
0
votes
1
answer
144
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Does the $3s$ orbital contain the $2s$ orbital?
The following image is in my introductory chemistry textbook:
It seems to imply that the $3s$ orbital “contains” the $2s$ and 1s orbital. That is, a $3s$ electron could find itself in a region of ...
- 375
0
votes
2
answers
402
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Hamiltonian of wavefunction of $2s$ and $2p$ orbitals
I have recently developed an interest in the analysis of a certain problem in atomic chemistry regarding the energies of $4s$ and $3d$ orbitals, and I observed that even though the wavefunction of $2s$...
- 11