My work focuses on the intersection of physics and computation. I use mathematical models to simulate complex phenomena, ranging from the subatomic scale to the cosmic scale.

One of the fundamental equations I work with is the Schrödinger equation, which describes how the quantum state of a physical system changes with time:

$i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \hat{H} \Psi(\mathbf{r},t)$

By solving these equations numerically, we can visualize behaviors that are otherwise impossible to observe directly. This approach allows us to bridge the gap between theoretical predictions and experimental results.

In addition to quantum mechanics, I also explore classical systems like the harmonic oscillator, which can be described by the following differential equation:

$m \frac{d^2x}{dt^2} + kx = 0$

These simulations are not just mathematical exercises; they are tools for discovery. They help us understand the underlying principles of the universe and inspire new ways of thinking about physical reality.