4. Refer to the following one-dimensional quantum potential structure. In region 0 the potentialV = 0o; in regions I and III the potential V = 0; in region II the potential V = V, = 1.0 eV. Thewidth of region I, L, = 2.0 nm; the width of region II, AL = L, - L = 1.0 nm, or L, = 1.5 L,.There is an electron in region I.V = VoIIIIX = 0X = L,X = L2(1) Show Schrodinger equations of the electron inside regions I, II, and III. |(2) Find initial solutions of the above equations with 6 unknown constants.(3) Find two out of six constants of the above solutions.(4) Find the next three constants of the solutions in step 2.(5) Find the allowed energy levels of the electron in region I in a unit of eV.(6) Find the last constant of the solutions in step 2.(7) Find the complete solutions for the three wave functions.(8) Find the expectation value of x at the ground state region I.(9) Calculate the transmission coefficient by using T = |Y m¥;?.III(10) Calculate the probability to find the electron at the first excited state from x = 3 nm to x =3.2 nm.

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