- 8

- 0

**1. Homework Statement**

For the ground state of a particle moving freely in a one-dimensional box 0≤x≤L with rigid reflecting end points, the uncertainity product (Δx)(Δp) is

(A) h/2

(B) h√2

(C) >h/2

(D) h/√3

**2. Homework Equations**

The uncertainity principle says that -

(Δx)(Δp) ≥ ħ/2

Ground state energy in a one dimentional box of size L is E = π

^{2}ħ

^{2}/(2mL

^{2})

**3. The Attempt at a Solution**

The particle will be localised in the resion between 0 and L. So the positional uncertainity is L

(Δx) =L

Particle is in the ground state

E= π

^{2}ħ

^{2}/(2mL

^{2})

p

^{2}/(2m) = π

^{2}ħ

^{2}/(2mL

^{2})

From here I have calculated the momentum ( p= πħ/L) of the particle but I cannot find the uncertainity in position. Can you give me a direction.