Quantum mechanics: what does d<x>/dt mean physically?

[gennes77]

Homework Statement

I am reading the Griffths book on quantum mechanics. In the first chapter on Momentum (Sect 1.5) what does d<x>/dt mean in the physical sense?

Homework Equations

NA

The Attempt at a Solution

If the expectation value <x> is already determined by the Schrödinger equation,

(i) thus <x> must be in the form of a number and hence d<x>/dt must equal to zero always. So calculating d<x>/dt is not relevant.

(ii) unless we are saying <x> changes in time but this will contradict my above statement... since the expectation is fixed once the wave function of a particle is known)

(iii) If this rate of change is about when the initial measurement is made and <x> spikes to one of the eigenvalues and then 'smears off' into the original wave function form, then my question is (from a mathematics perspective) how does the equation allow for a change from a non continuous form (when ψ collapses and <x> spikes) and then into a continuous form (when ψ goes back to its original form and <x> becomes the expectation value of ALL possible eigenvalues)

Thanks very much for any assistance!

gennes77

 

[Muphrid]

$\langle x \rangle$ is necessarily not a function of position, but it can still be a function of time for time-dependent wavefunctions.