EC2 instance type Updated 2025-07-16
Amazon's informtion about their own intances is so bad and non-public that this was created: instances.vantage.sh/
Inward Bound by Abraham Pais (1988) Updated 2025-07-16
The book unfortunately does not cover the history of quantum mechanics very, the author specifically says that this will not be covered, the focus is more on particles/forces. But there are still some mentions.
Lie algebra of Updated 2025-07-16
We can reach it by taking the rotations in three directions, e.g. a rotation around the z axis:
then we derive and evaluate at 0:
therefore represents the infinitesimal rotation.
Note that the exponential map reverses this and gives a finite rotation around the Z axis back from the infinitesimal generator :
Repeating the same process for the other directions gives:
We have now found 3 linearly independent elements of the Lie algebra, and since has dimension 3, we are done.
Rydberg atom Updated 2025-07-16
The projects you do must always aim to achieving some novel result.
You don't have to necessarily reach it. But you must aim for it.
Novel result can be taken broadly.
E.g., a new tutorial that explains something in a way never done before is novel.
But there must be something to your project that has never been done before.
You can start by reproducing other's work.
Fine structure Updated 2025-07-16
Split in energy levels due to interaction between electron up or down spin and the electron orbitals.
Numerically explained by the Dirac equation when solving it for the hydrogen atom, and it is one of the main triumphs of the theory.
Switzerland Updated 2025-07-16
Angular momentum operator Updated 2025-07-16
Basically the operators are just analogous to the classical ones e.g. the classical:
becomes:
Besides the angular momentum in each direction, we also have the total angular momentum:
Then you have to understand what each one of those does to the each atomic orbital:
There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
Long Island Updated 2025-07-16
Lord Kelvin Updated 2025-07-16

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