These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz
Question 1 Finite potential well Use this information to answer Question 1-2:
Consider an electron in a finite potential with a depth of V0=0.3eV and a width of 10nm. Find the lowest energy level. Give your answer in unit of eV. Answers within 5% error will be considered correct. Note that in the lecture titled “Finite Potential Well”, the potential well is defined from −L to L, which makes the well width 2L.
Answer: 0.0032741
Question 2 Finite potential well
Find the second lowest energy level. Give your answer in unit of eV. Answers within 5% error will be considered correct.
Answer: 0.013096
Question 3 Potential step
Consider a potential step with a height of V0=0.2eV. An electron is incident from the lower potential side (where the potential energy is set to equal to zero) with an energy E=0.3eV. Calculate the reflection probability.
Answer: 0.0718
Question 4 Potential step
Consider a potential step with a height of V0=0.5eV. An electron is incident from the lower potential side (where the potential energy is set to equal to zero) with an energy E=0.3eV. Find the penetration depth which is defined as the distance into the barrier region at which the probability decreases to 1/e of its initial value at the potential discontinuity, z=0. Give your answer in unit of nm. Answers within 5% error will be considered correct.
Answer: 0.2175
These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz
A non-classical behavior found in the potential step problem is that there is a finite reflection even when the potential step is negative. That is, an electron may reflect at the boundary even when it is incident in the region of higher potential, as shown below.
Calculate the reflection probability when E=0.1eV and V0=0.5eV. Answers within 5% error will be considered correct.
Answer: 0.1766
These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz
Question 6 Potential barrier
Consider a potential barrier with height V0=1eV and width L=1nm. Find the energy of incident electron at which the reflection probability is 95%. Give your answer in unit of eV. Answers within 5% error will be considered correct.
Answer: 0.8965
These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz
Question 7 Negative potential barrier
Consider a negative potential barrier with V0=−1eV and L=1nm. Find the lowest energy of incident electron at which the transmission probability becomes unity. Give your answer in unit of eV. Answers within 5% error will be considered correct. Note this is a finite potential well problem with electron energy greater than the well depth.
Answer: 0.51
These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz
