4) Consider the potential shown below, with two different potential steps V₁ and V2. An electron with an energy of E (V₁<E<V2) is incident from the left. Answer the following. V₁<E< V₂ Reg 1 Reg 2 Reg 3 0 a a) Write down the wave vectors in each region, in terms of the energy and the potential step heights. b) Draw the wave function (you can use the real part or the probability density) in region 1, 2 and 3 in the same plot. c) Estimate the overall transmission and reflection coefficient of the potential. (hint: you don't need to solve the wave functions to estimate R and T). d) (Extra credit: 3 marks) Solve the wave function in each region by applying the appropriate boundary conditions.

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4) Consider the potential shown below, with two different potential steps V₁ and V2. An electron with an energy of E (V₁<E<V2) is incident from the left. Answer the following. V₁<E< V₂ Reg 1 Reg 2 Reg 3 0 a a) Write down the wave vectors in each region, in terms of the energy and the potential step heights. b) Draw the