Consider a quantum wire along the x direction, with a confining po- tential V() = -Vo <0 for 0 < y² + 2² ≤ a², V(r) = 0

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Consider A Quantum Wire Along The X Direction With A Confining Po Tential V Vo 0 For 0 Y 2 A V R 0 1 (39.86 KiB) Viewed 39 times

Consider a quantum wire along the x direction, with a confining po- tential V() = -Vo <0 for 0 < y² + 2² ≤ a², V(r) = 0 for y² + x² > a². (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 Vo→∞, obtain the bound state energies in the yz plane explicitly for the ground state and first five excited states.