Knowlton
MSE 510
Quiz 4 – Learning objectives
Topics:
• Lectures of course on the introduction to quantum mechanics
Learning Objectives: For the quiz, the student should know how to:
• Mathematically show the relationship between the potential energy and the force
due to a potential energy
• Use bra-ket or Dirac notation
• Normalize a wavefunction
• Determine the single eigenvalue of the system given the operator and
wavefunction
• Determine the expectation value (i.e., average value) of an eigenvalue given the
operator and wavefunction
• Determine J, the probability current density (see equation sheet) for an incident,
reflected and transmitted electron
• Determine the Transmission Coefficient, T, and the Reflection Coefficient, R, and
their sum.
• Potential Barrier Problems: know how to sketch the potential with
corresponding wave functions with arrows and coefficients, regions, boundaries,
energies and k-values. This includes the following types of barriers
o Infinite well (i.e, particle in the box, quantum well)
 Additionally, determine the energies and delta-energies for a
quantum well and a function of n, the principle quantum number.
 Additionally, determine the allowed k’s as a function of n, the
principle quantum number
o Potential step (i.e., infinite potential step)
o Finite potential step