Ciro Santilli @cirosantilli 35

Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.

I.e.: they are both:

Lecture notes: Quantum Field Theory lecture notes by David Tong (2007).

By David Tong.

14 1 hours 20 minute lectures.

The video resolution is extremely low, with images glued as he moves away from what he wrote :-) The beauty of the early Internet.

This book really tries to recall basic things to ensure that the reader will be able to understand the more advanced ones.

Sometimes it goes a little bit overboard, like defining what a function does several times.

But Ciro Santilli really prefers it when authors error on the side of obvious.

This is very widely used in courses as of 2020, it became kind of the default book.

Unfortunately, this approach bores Ciro Santilli to death. Or perhaps is too just advanced for him to appreciate. Either of those.

800+ pages.

Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!

The private key is made of two randomly generated prime numbers: $p$ and $q$. How such large primes are found: how large primes are found for RSA.

The public key is made of:

Given a plaintext message m, the encrypted ciphertext version is:This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.

The inverse operation of finding the private m from the public c, e and $n$ is however believed to be a hard problem without knowing the factors of n.

However, if we know the private p and q, we can solve the problem. As follows.

First we calculate the modular multiplicative inverse. TODO continue.

Bibliography:

A way to write the wavefunction $\psi (x)$ such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:

If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:

Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.

The most important type of lens is the biconvex spherical lens.

A sequence of mRNA that can actually be transcribed.

For an example, see E. Coli K-12 MG1655 operon thrLABC.

Multiple different transcription units can be produced by a single operon, see: operon vs transcription unit.

NCBI online tool to find and view all open reading frames in a given FASTA: www.ncbi.nlm.nih.gov/orffinder/

Interesting because of the Cook-Levin theorem: if only a single NP-complete problem were in P, then all NP-complete problems would also be P!

We all know the answer for this: either false or independent.