Quantum mechanics is weird. In Schrödinger's model
for particle mechanics, our classical position function $x(t)$ is replaced with
a statistical object that we call the wavefunction $ \Psi(x,t)$.
Classical and quantum mechanical information about a system are not obtained from the same mathematical object:
- In Classical Mechanics: all information about a system is encoded
in its position function $x(t)$. Solves a second-order ordinary differentail equation.
- In Schrödinger's Quantum Mechanics: information about system energy is encoded
instead in the wavefunction $\Psi(x,t)$. Solves a linear partial differential equation.
Motion in Newtonian Mechanics