Measurement of position of particle Say a particle was found to be at $C$. If I measure the position of particle immediately, its given in Griffith's book that it will still be at $C$. In the macroscopic world, isnt this true only if the particle is at rest? Does this mean that the particle is at rest in the microscopic world as well?

 A: I think he (Griffiths) means that the observables are continuous in time. If we make a measurement immediately after the first, that is an infinitesimal time interval later, because of continuity, the value of the observable in the second measurement must be arbitrarily close to the first.
A: Well, position, momentum etc are non-normalizable. That's the reason why you wouldn't get exactly the same value everytime you measure after the first measurement but rather get a "spread" that would be dependent on the imprecesion of the measuring device. So you'd get linear combination of a tight range of wavefunctions(more precise your measuring device the tighter the range) rather than one value C.
The C referred to in the Griffith's book is for normalizable wavefunctions. 
A: First of all rest is obviously a relative term. That being said measurement changes the system, it's the transference of information if you will. So it is impossible for a system to know anything about another without affecting it.
That being said a particle could show up in the same even if it were "moving" due to the statistical properties of QM. The "same place" also being an ambiguous term. To what degree of precision?
A: 
Say a particle was found to be at C. If I measure the position of particle immediately, its given in griffith's book that it will still be at C. In the macroscopic world, isnt this true only if the particle is at rest? Does this mean that the particle is at rest in the microscopic world as well?

The keyword is immediately, no matter what position or momentum the particle has. Before you measure it, it is in a certain superposition of states. As soon as you measure it, it drops to one state. 
Right, you have measured it. You have taken your eye off it for even a split second. So there is a tiny probability, increasing over time, that it will drift away from that measured state, even if it was travelling at any arbitrary velocity.
In the classical world, the same idea applies, but with much less probability, so a soccer ball will almost certainly be in the same state 5 seconds after you measure it, but you can't apply this confidence level to quantum particles. 
A: What Griffiths means by "immediately" is that the second measurement is made after the first one after a time interval $dt \to 0$ where $dt$ is the time interval separating the two measurements.
