# Free particle wavefunction represent a fixed profile= wavepacket?

1. Nov 3, 2013

### Outrageous

Why the Griffiths book says : any function of x and t that depends on these variables in the special combination (x±vt) represent a wave of fixed profile, traveling in the -+x direction at speed v...
I don't really get the reason why from 2 terms of wavefunction can become only one term?

Thanks

File size:
34.3 KB
Views:
97
2. Nov 3, 2013

### vanhees71

Griffiths means that your wave function is either of the form $\psi(t,x)=f(x-v t)$ or of the form $\psi(t,x)=f(x+v t)$. Obviously the shape of the wave stays the same for each time, but it's moving to the right or left, respectively.

3. Nov 3, 2013

### Outrageous

How do you know there are two form of wavefunction?
By drawing out a graph of wavefunction against x? To see they are actually two superposition of two traveling wave?
Those information are from the wave function? How do you know? Do I miss any wave knowledge? Where should I study these?