# Foundations of Quantum Mechanics | Week 2

**Course Name: Foundations of Quantum Mechanics**

**Course Link: Foundations of Quantum Mechanics**

#### These are answers of Foundations of Quantum Mechanics Coursera Week 2 Quiz

**Question 1Finite potential well**

Use this information to answer Question 1-2:

**Consider an electron in a finite potential with a depth of V _{0}=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 2Finite 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 3Potential 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 4Potential step**

**Consider a potential step with a height of V _{0}=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**

**Question 5Potential step**

**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 V _{0}=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 6Potential barrier**

**Consider a potential barrier with height V _{0}=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 7Negative potential barrier**

**Consider a negative potential barrier with V _{0}=−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**

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