= Quantum mechanics
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= Quantum mechanical
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= Quantum
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Quantum mechanics is quite a broad term. Perhaps it is best to start approaching it from the division into:
* : obviously the simpler one, and where you should start
* : more advanced, and arguably "less useful"
Key experiments that could not work without quantum mechanics: {full}.
Mathematics: there are a few models of increasing precision which could all be called "quantum mechanics":
*
*
*
feels that the [largest technological revolutions since the 1950's have been quantum related], and will continue to be for a while, from deeper understanding of chemistry and materials to , understanding and controlling quantum systems is where the most interesting frontier of technology lies.
= Quantum mechanics experiment
{parent=Quantum mechanics}
Atoms exist and last for a long time, while in [classical electromagnetic theory punctual] orbiting electrons should emit radiation quickly and fall into the nucleus: https://physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit
In other sections:
* {child}
* {child} experiments, which are analogous to black body radiation experiments
*
* such as:
* {child}
Bibliography:
* http://web.mit.edu/course/5/5.73/oldwww/Fall04/notes/Experimental_Evidence_for_Quantum_Mechanics.pdf Experimental Evidence for Quantum Mechanics
= Emission spectrum
{parent=Quantum mechanics experiment}
{wiki}
= Atomic spectra
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= Spectral line
{parent=Emission spectrum}
{wiki}
A single line in the .
So precise, so , which makes no sense in !
Has been the leading motivation of the development of , all the way from the:
* : major lines predicted, including , but not finer line splits like
* : explains 2p spin split due to electron spin/orbit interactions, but not
* : explains
* : due to electron/nucleus spin interactions, offers a window into
= NIST Atomic Spectra Database
{c}
{parent=Spectral line}
database for : https://physics.nist.gov/PhysRefData/ASD/lines_form.html
Let's do a sanity check.
Searching for "H" for leads to: https://physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on
From there we can see for example the 1 to 2 lines:
* 1s to 2p: 121.5673644608 nm
* 1s to 2: 121.56701 nm TODO what does that $2$ mean?
* 1s to 2s: 121.5673123130200 TODO what does that mean?
We see that the table is sorted from lower from level first and then by upper level second.
So it is good to see that we are in the same 121nm ballpark as mentioned at .
TODO why I can't see 2s to 2p transitions there to get the ?
= Forbidden mechanism
{parent=Spectral line}
{wiki}
Bibliography:
* https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/12%3A_Time-Dependent_Perturbation_Theory/12.13%3A_Forbidden_Transitions from
= Selection rule
{parent=Forbidden mechanism}
{wiki}
https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/06%3A_Emission_and_Absorption_of_Photons/6.2%3A_Selection_Rules_and_Transition_Times has some very good mentions:
\Q[
So it appears that if a hydrogen atom emits a photon, it not only has to transition between two states whose energy difference matches the energy of the photon, but it is restricted in other ways as well, if its mode of radiation is to be dipole. For example, a hydrogen atom in its 3p state must drop to either the n=1 or n=2 energy level, to make the energy available to the photon. The n=2 energy level is 4-fold degenerate, and including the single n=1 state, the atom has five different states to which it can transition. But three of the states in the n=2 energy level have l=1 (the 2p states), so transitioning to these states does not involve a change in the angular momentum quantum number, and the dipole mode is not available.
So what's the big deal? Why doesn't the hydrogen atom just use a quadrupole or higher-order mode for this transition? It can, but the characteristic time for the dipole mode is so much shorter than that for the higher-order modes, that by the time the atom gets around to transitioning through a higher-order mode, it has usually already done so via dipole. All of this is statistical, of course, meaning that in a large collection of hydrogen atoms, many different modes of transitions will occur, but the vast majority of these will be dipole.
It turns out that examining details of these restrictions introduces a couple more. These come about from the conservation of angular momentum. It turns out that photons have an intrinsic angular momentum (spin) magnitude of $\hbar$, which means whenever a photon (emitted or absorbed) causes a transition in a hydrogen atom, the value of l must change (up or down) by exactly 1. This in turn restricts the changes that can occur to the magnetic quantum number: $m_l$ can change by no more than 1 (it can stay the same). We have dubbed these transition restrictions selection rules, which we summarize as:
$$
\Delta l = \pm 1, \Delta m_l = 0, \pm 1
$$
]
= Metastable electron
{parent=Selection rule}
A fundamental component of .
As mentioned at https://youtu.be/_JOchLyNO_w?t=581 from