**Unit 2: Principles of Quantum Theory**

*In the classical world, Newton’s laws and laws of conservation of
energy are used daily to predict the outcome of certain events. For
instance, the trajectory of a cannonball can be predicted with good
accuracy, given certain parameters such as the shooting angle, mass of
the cannonball, air resistance, and so forth. In the world of quantum
mechanics, where objects possess very small masses and move at high
speeds, the Schrodinger equation is used to predict the behavior of a
system comprised of quantum mechanical particles (electrons, nuclei,
etc.). Unlikely in classical mechanics, where the outcomes of the
calculations are undoubtedly clear (for instance, the cannon ball will
hit the ground at a precise coordinate point), the results of the
Schrodinger equation gives the probability of an event to occur. In the
quantum world, for a given set of parameters, a large number of events
can occur, and the Schrodinger equation will predict the probability
that such events will happen, given a distribution of results rather
than a single answer. In this unit, you will encounter the Schrodinger
equation for the first time.*

**Unit 2 Time Advisory**

This unit will take you 12.5 hours to complete.

☐ Subunit 2.1: 2.5 hours

☐ Subunit 2.2: 5 hours

☐ Subunit 2.3: 0.5 hours

☐ Subunit 2.4: 4.5 hours

**Unit2 Learning Outcomes**

Upon successful completion of this unit, the student will be able to:
- List and explain the fundamental postulates of quantum mechanics.
- Set up and solve the Schrodinger equation for a simple system.
- Mathematically prove Heisenberg’s uncertainty principle.
- Normalize the wavefunction of a system.
- Calculate the probability of finding the particle in a region of
space.

**2.1 Fundamental Postulates of Quantum Mechanics**
- **Reading: Washington State University: Professor Kirk Peterson’s
“Chem 332: Physical Chemistry II”**
Link: Washington State University: Professor Kirk Peterson’s “Chem
332: Physical Chemistry
II” (PDF)

Instructions: To access Professor Peterson’s resources, click on
the link and scroll down to the bottom of the webpage to the “Class
Recourses” heading. Select the “Postulates of Quantum Mechanics”
link to open the PDF file, and read and learn about these
postulates. Make sure you understand the “practical” meaning of
these equations, that is, why the wavefunction of a quantum
mechanical system is normalized, and so forth. These postulates
constitute the base of quantum mechanical problems and calculations.
Studying this resource should take approximately 1 hour to
complete.

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

**Reading: Georgia Institute of Technology: Professor David Sherrill’s “Postulates of Quantum Mechanics”**Link: Georgia Institute of Technology: Professor David Sherrill’s “Postulates of Quantum Mechanics” (HTML)Instructions: Please click on the link to access Professor Sherrill’s resource, and read the entire webpage. Make sure you understand the “practical” meaning of these equations, that is, which physical observables (momentum, kinetic energy, etc.) are associated with Hermitian operators, and so forth. These postulates constitute the base of quantum mechanical problems and calculations. Studying this resource should take approximately 1 hour to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Lecture: YouTube: Dony Lee’s “QM0.1: Postulates of Quantum Mechanics”**Link: YouTube: Dony Lee’s “QM0.1: Postulates of Quantum Mechanics” (YouTube)Instructions: Please click on the link above, and watch the brief video lecture. This video covers the fundamental postulates of quantum mechanics; as for the above readings, make sure you understand the “practical” meaning of these equations and how they are used in quantum mechanical calculations. Studying this resource should take approximately 0.5 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.2 The Schrodinger Equation**
- **Reading: Everyscience.com’s “The One Dimensional Schrodinger
Equation”**
Links: Everyscience.com’s “The One Dimensional Schrodinger
Equation”
(HTML)

Instructions: Please click on the link and read the entire
webpage. While reading, solve the Hamiltonian following the steps
indicated in the reading. This provides a glance of the Schrodinger
equation. Studying this resource should take approximately 1 hour
to complete.

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

**Reading: Macquarie University: Professor James Cresser’s “Interference and Diffraction & Wave Mechanics” Lecture Notes**Link: Macquarie University: Professor James Cresser’s “Interference and Diffraction & Wave Mechanics” Lecture Notes (PDF)

Instructions: Please click on the link and select “Ch6: The Schrodinger Wave Equation” to download the PDF file, and read the entire text (18 pages). While reading, following the math steps indicated in the reading to find the wavefunction of the system by solving the Hamiltonian. Also make sure you understand important concepts such as boundary and continuity conditions. Professor Cresser’s notes provide a deeper explanation of the Schrodinger equation. Studying this resource should take approximately 3 hours to compete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Reading: YouTube: Praba Siva’s “Schrodinger Equation – Step Wise Derivation Part 1/3,” “Part 2/3,” and “Part 3/3”**Links: YouTube: Praba Siva’s “Schrodinger Equation – Step Wise Derivation Part 1/3”, “Part 2/3”, and “Part 3/3” (YouTube)

Instructions: Watch these three videos. While watching the videos, follow the instructor by doing the same math on a sheet of paper until you are comfortable deriving the Schrodinger equation on your own. This video tutorial shows a step-by-step derivation of the Schrodinger equation. Studying these resources should take approximately 1 hour to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Assessment: The Saylor Foundation’s “Assessment 3”**Link: The Saylor Foundation’s “Assessment 3” (DOC)

Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).

Completing this assessment should take approximately 1 hour.

**2.3 Wavefunctions and the Born Interpretation**
- **Reading: Everyscience.com’s “Wavefunctions and the Born
Interpretation”**
Link: Everyscience.com’s “Wavefunctions and the Born
Interpretation”
(HTML)

```
Instructions: Clink on the above link to access the webpage.
Please read the entire webpage and note the role of the
wavefunction as the “source of all measurable information of a
quantum mechanical system.” Studying this resource should take
approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**2.4 Wave Functions and the Heisenberg’s Uncertainty Principles**
- **Reading: Robert B. Griffiths’s “Consistent Quantum Theory”**
Link: Robert B. Griffiths’s “Consistent Quantum
Theory” (PDF)

Instructions: Please click on the link, find “Chapter 2: Wave
Functions,” select the PDF link for the text, and read sections
2.1–2.4. This resource explains the physical interpretation of the
wavefunction. Studying this resource should take approximately 2.0
hours to complete.

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

**Reading: Macquarie University: Professor James Cresser’s “The Wave Function” Lecture Notes**Links: Macquarie University: Professor James Cresser’s “The Wave Function” Lecture Notes (PDF)

Instructions: Please click on the link, select the link to “Ch3: The Wave Function” to access the PDF file, and read the entire chapter (8 pages). Make sure you understand the concept of “probability waves” and the derivation of the Heisenberg uncertainty principle. Studying this resource should take approximately 1.5 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Reading: Everyscience.com’s “Heisenberg’s Uncertainty Principle”**Link: Everyscience.com’s “Heisenberg’s Uncertainty Principle” (HTML)

Instructions: Please click on the link and read the entire webpage for a quick explanation and useful review of “Heisenberg’s Uncertainty Principle.” This resource is useful to quickly review the mathematical proof of the Uncertainly Principle. Make sure you know how to derive the uncertainty in momentum and position. Studying this resource should take approximately 0.5 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Web Media: YouTube: Physics Academy’s “Quantum Mechanics 008: Measurement and Heisenberg’s Uncertainty Principle”**Link: YouTube: Physics Academy’s “Quantum Mechanics 008: Measurement and Heisenberg’s Uncertainty Principle” (YouTube)

Instructions: Please click on the link above, and watch the video. This short video tutorial covers the concept of measurement via entanglement, the double slit experiment, and Heisenberg’s uncertainty principle. Studying this resource should take approximately 0.5 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Assessment: The Saylor Foundation’s “Assessment 4”**Link: The Saylor Foundation’s “Assessment 4” (DOC)

Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).

Completing this assessment should take approximately 1 hour.