Texte intégral
A free particle with massmis confined in an infinite symmetric potential well with length 2L:
V(x) =
∞ (x≤ −L)
0 (−L≤x≤L)
∞ (x≥L)
1. Derive the wave function ψn(x, t) for the particle, and express your answer in terms of sine and cosine.
2. Calculateρ(x, t) andJ(x, t).
3. Calculatehˆxi,hˆpiandhHˆi.
4. Calculate (∆ˆx)2, (∆ˆp)2and (∆ ˆH)2. 5. Verify that (∆ˆx)(∆ˆp)≥ 12¯h.
1
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