Welcome to the quantum realm! Here, particles obey the laws of quantum mechanics, where probability rules and classical intuition breaks down. The state of a quantum system is described by its wavefunction \(\psi(x,y,t)\), which contains all possible information about the system.
Key Quantum Equations:
Time-dependent Schrödinger equation:
$i\hbar\frac{\partial}{\partial t}\psi = -\frac{\hbar^2}{2m}\nabla^2\psi + V\psi$
Probability density:
$P(x,y,t) = |\psi(x,y,t)|^2$
Heisenberg Uncertainty:
$\Delta x \Delta p \geq \frac{\hbar}{2}$
In this visualization, you're watching a quantum wave packet evolve. The brightness shows the probability density |\(\psi\)|², representing where you might find the particle if you measure it.
The wave packet's initial state is a Gaussian wave packet with momentum \(p\): $\psi(x,y,0) = A\exp\left(-\frac{(x-x_0)^2 + (y-y_0)^2}{4\sigma^2}\right)\exp\left(\frac{ipx}{\hbar}\right)$