Consider a square well having an infinite wall at z = 0 (infinite potential for x...

  

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Consider a square well having an infinite wall at z = 0 (infinite potential for x < 0) and a wall height U for r > L (and U(x) = 0 inside the well, 0≤x≤L), as shown below. 0 L U E (a) For the case E <U, obtain solutions to the Schrödinger equation inside the well and in the region beyond (x > L) that satisfy the appropriate boundary conditions at z = 0 and x = ∞0. [2] (b) Enforce the proper matching conditions at x = L to find an equation for the allowed energies of the system. (c) Are there conditions for which no solution is possible? Explain. [2] [2] Consider a square well having an infinite wall at z = 0 (infinite potential for x < 0) and a wall height U for r > L (and U(x) = 0 inside the well, 0≤x≤L), as shown below. 0 L U E (a) For the case E <U, obtain solutions to the Schrödinger equation inside the well and in the region beyond (x > L) that satisfy the appropriate boundary conditions at z = 0 and x = ∞0. [2] (b) Enforce the proper matching conditions at x = L to find an equation for the allowed energies of the system. (c) Are there conditions for which no solution is possible? Explain. [2] [2]

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