In Classical physics, particles are pure points, which form World-lines through Spacetime. Conversely, Quantum physics pictures particles as Wave Functions which are extended in space. Are Wave Functions extended in time, too ?

 

Well in general they persist for more than an instant.

Schrödinger's equation is time-dependent.

[math]\frac{\delta}{\delta t}[/math][math]\int[/math][math]\psi[/math]

Edited March 17, 201015 yr by swansont
fix LaTEx syntax error

If the potential is not a function of time (i.e. function of space only), then schrodinger equation will be solved by separation of variables, and the time function will be only a phase function (exp(-iE*t/hbar)).

However, if the potential is function of time, then the solution will be more complicated and the maximum of the probability density function will be moving with time through space; which gives the analogy to motion in classical physics.