2. Consider the ID potential which has a centered infinite square well with a delta- function barrier in the middle: а s

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2. Consider the ID potential which has a centered infinite square well with a delta- function barrier in the middle: а soo, for | >a V(2) = | a8(x), for |z| <a, where a is a positive constant. (a) Write down the general form of the energy eigenfunction in the regions 0 < x <a and -a< x < 0. (b) What are the four boundary conditions that the wave function must satisfy in these two regions, including the one arising from the 8(x) function at the origin? (5) (c) When is a quantum system “bound”? Give a condition in terms of the system energy E and potential energy V. (2) (d) What is tunnelling? Describe explicitly a situation which distinguishes classical physics from quantum mechanics. (3)