#3. Quantum Well in 2-D Space (35 pts) 1) (5 points) Solve the time-independent Schrödinger equation for a 1D infinite p

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3 Quantum Well In 2 D Space 35 Pts 1 5 Points Solve The Time Independent Schrodinger Equation For A 1d Infinite P 1 (107.14 KiB) Viewed 30 times

#3. Quantum Well in 2-D Space (35 pts) 1) (5 points) Solve the time-independent Schrödinger equation for a 1D infinite potential well with length a. Assume potential energy is zero in the well, and infinity outside the well. Find the wavefunction and energy. 2) (5 points) What is the length in k-space that each state determined by 1) occupies? 3) (5 points) Based upon results from 1) and 2), calculate the density of states of an electron in one dimension. Now, consider a quantum well in two-dimensional space as shown below. The potential V(x, y) = 0 for 0 < x <a, and is infinity everywhere else. V=0 V=0 V=0 x=0 x=a 4) (10 points) Assuming that the wavefunction is of the form u(x)eiky, calculate and sketch the E-k diagram of the electron from E = 0 to E = () 2 872 (ಐ. 2m 8n2 5) (10 points) Calculate and sketch the density of states from E = 0 to E = 2m