Question

For a particle In a one dimension box, if uncertainty in position of the particle is 5% then what will be the percentage uncertainty in the energy of the particle?

Answer 1

@Vincent-Lyon.Fr

Answer 2

@Abhisar
@perl

Answer 3

Relative uncertainty cannot be used in the uncertainty relation. you must know the size of the box. 5% of what? a meter, a micron, a femto-meter each will have a different absolute uncertainty in position and therefore in momentum and energy

Answer 4

@gleem is right, but if I had to hazard a guess I'd imagine that the uncertainty is 5% of the length of the box, in which case the uncertainty in momentum can be calculated. Knowledge of the uncertainty in energy, however, is a different matter.

Answer 5

take the length of the box to be L. Now how to do it?

Answer 6

You can calculate the uncertainty in momentum to be
\[ \Delta p = \frac{\hbar}{2\Delta x} = \frac{\hbar}{2 \cdot 0.05 \cdot L}\]
But a knowledge of the uncertainty in energy requires a knowledge of the state that the particle occupies.

Answer 7

And of course, this is the minimum uncertainty - to be more correct, replace the first
\(=\) with \(\geq\).

Answer 8

there is some math processing error, i cant see it