Suppose that the wavefunction of an electron in a carbon nanotube is a linear combination of cos(nx) functions.

(a) Use mathematical software, a spreadsheet, or the Living graphs on the web site of this book to construct superpositions of cosine functions as

where the constant 1/N is introduced to keep the superpositions with the same overall magnitude. Set x=0 at the centre of the screen and build the superposition there.

(b) Explore how the probability density ψ²(x) changes with the value of N.

(c) Evaluate the root mean square location of the packet, 〈x²〉^1/2.

(d) Determine the probability that a given momentum will be observed.

Transcribed Image Text:

N ψ(x)=- Η Σcs(knx) N k=1