Zero-point Energy

• Minimum energy corresponds to n=1

• n=0 => ?n(x)=0 for all x

• => P(x)=0 => no electron in the well

• zero-point energy

• never at rest!

• Uncertainty principle: if ?x=L/?, then ?px > h/(?x) = ? h /L => E > (?px )2/2m = ? 2 h 2/2mL2 = h2/(8mL2)

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