Cylindrical quantum wire. Consider a quantum wire along the x direction, with a confining po- tential V (m) = -Vo < 0 fo

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Cylindrical Quantum Wire Consider A Quantum Wire Along The X Direction With A Confining Po Tential V M Vo 0 Fo 1 (86.94 KiB) Viewed 34 times

Cylindrical quantum wire. Consider a quantum wire along the x direction, with a confining po- tential V (m) = -Vo < 0 for 0 < y2 +z2 <a?, V(m) = 0 for y2 + x2 > a?. (a) Through a suitable separation of variables obtain the form of both the scattering and bound states in this potential. Write down the conditions that would determine the reflection amplitude and the binding energies (do not attempt a solution). (b) In the limit V +00, obtain the bound state energies in the yz plane explicitly for the ground state and first five excited states.