Introduction of the Dirac notation and postulates of QM

Recently I have finished a project, with many help from my graduate student mentor. I worked on the assessment of DFT on the spatial variance of molecules. You can read more at https://arxiv.org/abs/2011.12561. I also have to start a new category because of this post, and I hope this won’t be the last post in this category. Enjoy!

Notes on angular momentum.

Notes on the Variational principle.

Midterm practice Short Questions Write the time dependent Schrödinger equation in three dimensions and the position representation for a free particle. Write the time independent Schrödinger equation in three dimensions and the position representation for a free particle. Give the eigenfunctions and eigenvalues. Given an operator $\hat{O}$, give its expectation value for state $\ket{\psi}$ in bra-ket notation, and in the position and momentum representations. You can write $\bra{\vec{r}}\psi\rangle = \psi(\vec{r})$ and $\bra{\vec{p}}\psi\rangle = \psi(\vec{p})$

Notes on solving the quantum harmonic oscillator.

Dirac: 'A measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured.'