Author Archives: wdengquantum.me

The goal of physics is to understand the what, how, and why of the universe. The twist is that sometimes one sometimes has to introduce auxiliary physical quantities as stepping stones towards such an understanding. An exemplar of this in … Continue reading →

Having been a member of Cambridge University Spaceflight (CUSF) during my first year as an undergraduate student, I thought it would be fun to document all the knowledge I’ve acquired with regards to the art of high-power rocketry. A good … Continue reading →

The purpose of this post is to explain the Born-Oppenheimer approximation. Ignoring relativistic fine/hyperfine structure effects, the gross structure molecular Hamiltonian \(H\) (i.e. the “theory of everything”) is: \[H=T_{\text n}+H_{\text e}\] where the nuclear kinetic energy is: \[T_{\text n}=\sum_{i}\frac{\textbf P_i^2}{2M_i}\] … Continue reading →

In this interview, well-known theoretical physicist Frank Wilczek commented that “still to this day I think the quantum theory of angular momentum is one of the absolute pinnacles of human achievement. Just beautiful”. The purpose of this post is to … Continue reading →

The purpose of this post will be to review a standard method for passing from the classical to the quantum world (or more poetically, turning \(\hbar=0\) on to \(\hbar=1\) in natural units). This procedure is called canonical quantization. It is … Continue reading →

The Shapes and Structures of Molecules Also, spin angular momentum coupling between \(^{13}\text C\) nuclei and \(^1\text H\) nuclei are typically suppressed via broadband proton decoupling. Also, due to low isotopic abundance, spin angular momentum coupling among \(^{13}\text C\) nuclei … Continue reading →

If one has a collection \(Q=\int\rho d^3x>0\) of positive charge \(\rho>0\) in some region of space, then the electric dipole moment \(\textbf p\) of \(Q\) may be viewed as \(\textbf p=Q\textbf X\), where \(\textbf X=\frac{1}{Q}\int\textbf x\rho d^3x\) is the center … Continue reading →

Problem: What is a lattice \(\Lambda\)? What does it mean to say that a lattice is Bravais? Give an example of a Bravais lattice and a non-Bravais lattice. Solution: A lattice \(\Lambda\) is any periodic set of lattice points in … Continue reading →

Problem: What does it mean for a collection of feature vectors \(\mathbf x_1,…,\mathbf x_{T}\) to represent a form of sequence data. Give some examples of sequence data. Solution: It means that the feature vectors are not i.i.d.; indeed, they are … Continue reading →

Problem: Where and why should one create an __init__.py file? Solution: Inside a folder/directory that’s meant to be a Python package containing a bunch of Python modules with useful functions, etc. that other Python scripts would be importing from (not … Continue reading →