MSE 510
Electrical, Optical & Dielectric Materials
Dept. of Materials Science & Engineering
Spring 2015/Bill Knowlton
Project 3
Project 3 is a team-based project so you may form teams of 2-3 and submit one project per team.
You will need to organize your team – I will not appoint them. See due dates and deliverables at the
end of this document.
In Project 3, you will explore and implement the following 3 aspects (see Hints):
1 Complex math numbers and math (see for example page 865 of your book) that incorporate
quantum mechanical wave functions.
2 Use a mathematical program that defines Mathematical operators that operate on quantum
mechanical wave functions.
3 Solving a system of equations and extracting a specific solution or set of solutions from the
list of solutions - These systems of equations should come from boundary conditions defined
by one of the 1 dimensional potential energy barrier problems in quantum mechanics (that we
have covered or others).
Use Mathematica or a mathematical program to analyze and explore these three topics in depth by
providing well described examples. The examples can be both mathematical and graphical (e.g.,
plots, Manipulate[ ] plots, etc.) in nature. Start with a simple example or two, and then move toward
more complicated examples that involve quantum mechanics. Complicated examples include, but
are not limited to, the following:
• Operators that have been defined in your mathematical program that operate on a wave
function to determine an eigenvalue of interest (e.g., Energy, momentum, position)
• Normalize a wave function (e.g., normalizing a wave function for a hydrogen atom which
requires spherical coordinates) then plot the wave function.
• Find the expectation value (e.g., Energy, momentum, position), thus use the operators that
have been defined in your mathematical program to operate on wave functions.
• Finding or proving the Heisenberg Uncertainty Principle for a particular wave function (i.e.
Δx·Δp ≥ ћ), thus use the operators that have been defined in your mathematical program to
operate on wave functions.
• Find the Probability Current Density, J, for a particular wave function by defining the
operator J that operates on a wave function. Thus, use the operators that have been defined in
your mathematical program to operate on wave functions.
• Solve for the coefficients of wave functions using boundary conditions, then plot the wave
function. Thus, use the operators that have been defined in your mathematical program to
operate on wave functions.
See books on Physical Chemistry or Quantum Physics, Quantum Chemistry or Quantum Mechanics.
Use the same format you have used for your first two projects. So include an abstract, thorough
discussion of your examples, applications section, conclusions, and reference section. No need to
include an error analysis section unless it is appropriate. You will be graded using the same grading
sheet as in the first two projects.
Hint:
If you are using Mathematica, you can use the following examples to help you.
• Complex math numbers and math –Module 5 on the course website
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MSE 510
Electrical, Optical & Dielectric Materials
•
•
Dept. of Materials Science & Engineering
Spring 2015/Bill Knowlton
Defining mathematical operators – see for example Module 5 on the course website
Solving a system of equations and extracting a specific solution or set of solutions from the
list of solutions – see Module 3 (introduction) and Module 10 (advanced) on the course
website
Due date:
• Due Sunday, 2/8, 5pm; Email me the following
o A list of your team members. Thus, you need to organize your team and choose the
person in charge of corresponding (email) with me.
• Due Thursday, 2/12 before class; Email me:
o Final project in pdf format. Send me the Mathematica file if you used Mathematica.
o
Each of you will email me a completed and signed Self-Evaluation form
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