- #1
Abhishek11235
- 175
- 39
In Griffiths,Quantum Mechanics 2nd edition,Chapter 2,he gives a problem to calculate the revival time of a wave. Revival time is defined as the time taken by a wave to go from one side(x=0) to other side(x=a). Now let's calculate the revival time with 2 methods.
Method 1:
Now to go from 1 position to other and coming back to same place is 1 oscillation. The time period of Oscillation is:
$$T= 2π/\omega $$
We have $$E= 1/2 ka^2$$ where E is energy and a is width or amplitude. Since $$k=m(\omega)^2$$ we have after substituting in energy equation and then in the Equation for time period we find:
$$T= \sqrt{2m/E}×a×π$$
Method 2:
Now,by defination,the particle covers distance 2a with average velocity v given by:
$$v=\sqrt{2E/m}$$
So ##vT=2a## gives
$$T= a\sqrt{2E/m}$$
The question is why the above 2 methods give different result?
After checking solution manual,I found method 2 answer to be correct.
Method 1:
Now to go from 1 position to other and coming back to same place is 1 oscillation. The time period of Oscillation is:
$$T= 2π/\omega $$
We have $$E= 1/2 ka^2$$ where E is energy and a is width or amplitude. Since $$k=m(\omega)^2$$ we have after substituting in energy equation and then in the Equation for time period we find:
$$T= \sqrt{2m/E}×a×π$$
Method 2:
Now,by defination,the particle covers distance 2a with average velocity v given by:
$$v=\sqrt{2E/m}$$
So ##vT=2a## gives
$$T= a\sqrt{2E/m}$$
The question is why the above 2 methods give different result?
After checking solution manual,I found method 2 answer to be correct.
Last edited: