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6.2(a) Complex functions of the form eikx can be used to model the wavefunctions of particles...

6.2(a) Complex functions of the form eikx can be used to model the wavefunctions of particles in a linear accelerator. Show that any linear combination of the complex functions e2ix and e−2ix is an eigenfunction of the operator d2/dx2 and identify its eigenvalue.

6.2(b) Functions of the form sin nx can be used to model the wavefunctions of electrons in a carbon nanotube. Show that any linear combination of the functions sin 3x and cos 3x is an eigenfunction of the operator d2/dx2 and identify its eigenvalue.

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