# 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 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.
Note that in the lecture titled “Finite Potential Well”, the potential well is defined from −L to L, which makes the well width 2L.

Question 2
Finite potential well

Find the second lowest energy level.

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.

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.

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

Question 5
Potential 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 V0​=0.5eV.
Answers within 5% error will be considered correct.

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%.

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.
Note this is a finite potential well problem with electron energy greater than the well depth.