“True happiness occurs only when you find the problems you enjoy having and enjoy solving”- Mark Manson
The thrust of my work as an M.Sc student is on generating Kohn-Sham potentials for chemical systems exhibiting considerable to significant multireference character.
Let’s start with something more tangible and relatable. Loosely speaking, classical mechanics is the study of the motion or behavior of macroscopic bodies (i.e. large objects), such as planets, desks, books, humans, to name a few. Unfortunately, classical mechanics fails miserably to explain the behavior of microscopic bodies (i.e. subatomic particles), such as protons, neutrons, and electrons, the latter being the most important to my research and are my favorite microscopic particle. People have favorite microscopic particles, right? Anyways, how do we remedy this problem? Does it even matter if we do? The answers to both questions are quantum mechanics and it absolutely does matter. The behavior of microscopic particles is governed by quantum mechanics, much like how the behavior of macroscopic particles is governed by classical mechanics. Consider an object of mass, \(m\), traveling along a wire, (let’s confine the mass’ movement to one-dimension, say along the \(x\)-axis). Part of the classical mechanical regime is to determine the position, \(x\), of the particle at any given time, \(t\), that is we’d like to know \(x(t)\). Once we know \(x(t)\), we get access to some goodies, like the velocity, \(v= \frac{dx}{dt}\), momentum, \(p=mv\), the kinetic energy, \(T=\frac{1}{2}mv^{2}\), and other dynamical quanities of the object.
The key entity in quantum mechanics is the wavefunction, from which we can attain all the information, or goodies about the system of interest. The wavefunction is an enigmatic entity, that is, its quite difficult to conceptualize. However, Dr. Chris Cramer cleverly describes the wavefunction as being an oracle that you ask questions to by means of probing it with a so-called operator. Most often we are interested in the total energy of the system of interest and it can be obtained by probing the wavefunction with the Hamiltonian operator. This operator is a sum of the kinetic energy operator and potential energy operator, where the latter characterizes the system and the former is the same for every system (more on this later). Now that we’ve introduced the wavefunction and the Hamiltonian operator, we’re ready to introduce the Schrodinger equation, the most central equation of quantum mechanics, given in \eqref{eqn1}.
\begin{equation} \label{eqn1} \boxed{\hat{H}\psi=E\psi} \end{equation} where \begin{equation} \boxed{\hat{H}= -\frac{\hbar}{2m}\nabla^2+V} \end{equation}
Interested in learning more about what I do? The following texts are indispensable to my research-check them out!
