Schrodinger Equation

The dynamics of a one-dimensional quantum system are governed by the time-dependent Schrodinger equation:

iℏ (∂ψ/∂t)= −(ℏ^2 /2m) x (∂^2ψ/∂x2) + Vψ

The wave function $\psi$ is a function of both position $x$ and time $t$, and is the fundamental description of the realm of the very small. Imagine we are following the motion of a single particle in one dimension. This wave function represents a probability of measuring the particle at a position $x$ at a time $t$. Quantum mechanics tells us that (contrary to our familiar classical reasoning) this probability is not a limitation of our knowledge of the system, but a reflection of an unavoidable uncertainty about the position and time of events in the realm of the very small.