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Unformatted text preview: (b) Physically what does the wave function in part (a) represent? • The probability of ﬁnding an electron at the point x . 2 marks 2 Sept. 29, 2009 ELEC 4705 Electronic Properties of Materials Quiz 1 3. Wave Packets (5 Marks) (a) Why do we represent an electron by a wave packet? • Because the free electron solution for a single phase is un-localized. (b) If ψ is deﬁned with respect to x (space) as: ψ ( x ) = e-( x-x ) 2 / 2(Δ x ) 2 (5) Sketch the wave function in the space. Gaussian distribution centered at x and with a width δx . What would be it’s functionality in k space? Sketch it as well. Gaussian distribution centered at k and with a width δk . 3 Sept. 29, 2009...
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- Winter '09
- gradient ∂V ∂x