I have study

The Book

This is the link to the first physics book I ever received: HERE!

(Obviously I’m not sending the book to you I’m just recommending it to you)

It’s nice introduction to Quantum Physics, even though some math are definitely missing, it does provide some sort of analogies and explanation which is decent.

Well I doubt I know how to do the exercises (I believe some of the stuff like Hermite polynomials are not covered yet in my course. (I think covered in Year 3? Not sure!)

Turns out they briefly touched upon Hermite Polynomials in Modern Physics course

After Year 3 I finally understand it…

From Luigi Del Debbio and Arjun Berera’s Quantum Mechanics books, they say:

Eigenfunctions of a quantum harmonic oscillator can be written as:

\[u_n(x)=C_n \exp \left\{-\alpha^2 x^2 / 2\right\} H_n(\alpha x)\]

\(\alpha^2 \equiv m \omega / \hbar\) and \(H_n(\alpha x)\) are polynomials of degree \(n\), known as Hermite polynomials. Once again using dimensional analysis, you can show that \(\alpha\) has got dimensions of inverse length, so that the product \(\alpha x\) is dimensionless. The Hermite polynomials satisfy the orthogonality relation

\[\int_{-\infty}^{\infty} \exp \left\{-s^2\right\} H_m(s) H_n(s) \mathrm{d} s=2^n \sqrt{\pi} n ! \delta_{m n},\]

The first few Hermite polynomials are:

\[\begin{aligned} & H_0(s)=1 \\ & H_1(s)=2 s \\ & H_2(s)=4 s^2-2 \\ & H_3(s)=8 s^3-12 s \end{aligned}\]

It’s a good introduction to Physics degree and it intensified my passion towards Physics (funny thing is I almost went to study Earth System Science… I might like typhoons, but oceans and stuff aren’t built for me… and I also hate labs so welp)

Slow Fast Large Small Physics

A short briefing:

  • Slow and “Large Scale” Physics -> Classical Mechanics
  • Slow and “Small Scale” Physics -> Quantum Mechanics
  • Fast and “Large Scale” Physics -> Relavistic Mechanics
  • Fast and “Small Scale” Physics -> Quantum Field Theory

I hate classical Mechanics (Dynamics are just terrible, except when it’s some interesting orbit stuff)

Relavistic Mechanics are more fun but also annoying

Quantum Mechanics is surprisingly fun but it’s assuming you get what’s happening

Quantum Field Theory, I don’t have the knowledge to comment on it!