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Unit 1: Origins of Quantum Theory  

Quantum mechanics originated in the late nineteenth century, when classical physics dramatically failed to explain certain experimental results.  The three main experimental observations that could not be explained by classical physics include phenomena related to the blackbody radiation, the photoelectric effect, and the emission of atomic spectra.  Although physicists initially tried to patch up classical theory, it gradually became clear that new ideas were necessary.  In this unit, you will learn in details about the origins of quantum mechanics.

Unit 1 Time Advisory
This unit will take you approximately 17.5 hours to complete.

☐    Subunit 1.1: 4 hours

☐    Subunit 1.2: 2 hours

☐    Subunit 1.3: 2 hours

☐    Subunit 1.4: 2 hours

☐    Subunit 1.5: 3 hours

☐    Subunit 1.6: 1 hour

Unit1 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

  • Solve eigenvalue equations.
  • Explain the difference between classical and quantum mechanics.
  • List and explain the three major experimental data that could not be explained by classical physics.
  • Describe the origins of quantum mechanics.
  • Explain wave-particle duality.
  • Solve problems involving the De Broglie equation.

1.1 Mathematical Review for Physical Chemistry  

  • 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: Please click on the link above, and scroll down to the bottom of the webpage to the “Class Resources” heading.  Select the “mini PChem math review” link to download the PDF file, and read the entire document (8 pages).  Review these mathematical methods useful to solve problems in Physical Chemistry.  Reading and taking notes on this text should take approximately 4 hours to complete.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2 Mathematical Concepts in Quantum Mechanics  

  • Reading: Everyscience.com’s “Principles of Quantum Mechanics” Link: Everyscience.com’s “Principles of Quantum Mechanics” (HTML)

    Instructions: Please click on the link above, and read this entire webpage, which provides mathematical tool useful to solve quantum mechanical problems.  Studying this resource should take approximately 2 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 1” Link: The Saylor Foundation’s “Assessment 1” (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.

1.3 Review of Classical Mechanics  

  • Web Media: YouTube: Stanford University: Leonard Susskind’s “Lecture 1 | Modern Physics: Classical Mechanics” Link: YouTube: Stanford University: Leonard Susskind’s “Lecture 1 | Modern Physics: Classical Mechanics” (YouTube)

    Instructions: Please click on the link above, and watch the entire video.  This lecture provides a good review of classical mechanics.  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: Rochester Institute of Technology: Professor Michael Richmond’s “Review of Classical Mechanics” Link: Rochester Institute of Technology: Professor Michael Richmond’s “Review of Classical Mechanics” (HTML)

    Instructions: Please click on the link above, and read the entire webpage.  This subunit is meant to be a quick review of classical mechanics concepts.  These concepts have been explained in detail in PHYS101 (algebra-based).  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.

1.4 The Failure of Classical Physics and the Origins of Quantum Mechanics  

  • Reading: Macquarie University: Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes Link: Macquarie University: Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes (PDF)
     
    Instructions: Please click on the link and select “Ch2: The Early History of Quantum Mechanics” to access the PDF file of the lecture notes.  While reading the material, take notes repeating the mathematical derivation of the Plank’s constant.  Professor Cresser’s notes provide an historical background on the origins of quantum mechanics.  Studying this resource should take approximately 0.75 hours to complete.  Note that this reading covers the material you need to know for subunit 1.4.4. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: Weber State University: Professor Bradley W. Carroll’s “Three Failures of Classical Physics” Link: Weber State University: Professor Bradley W. Carroll’s “Three Failures of Classical Physics” (HTML)
     
    Instructions: Please click on the link and read the entire webpage.  Make sure you understand why classical mechanics was inadequate at explaining certain experimental observations, that is, why electrons do not fall into the nucleus of an atom, and so forth.  Studying this resource should take approximately 1.25 hours to complete.  Note that this reading covers the material you need to know for subunits 1.4.1–1.4.4.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.4.1 Blackbody Radiation and the Ultraviolet Catastrophe   Note: This subunit is covered by the readings assigned beneath subunit 1.4.  In particular, please focus on Section 1 of Professor Carroll’s “Three Failures of Classical Physics” to learn about blackbody radiation.

1.4.2 The Photoelectric Effect   Note: This topic is covered by the reading assigned beneath subunit 1.4.  Please review Section 2 of Professor Carroll’s “Three Failures of Classical Physics” to learn about the photoelectric effect.

1.4.3 Atomic Spectra   Note: This topic is covered by the reading assigned beneath subunit 1.4.  Please review Section 3 of Professor Carroll’s “Three Failures of Classical Physics” to learn about the inability of classical physics to explain the emission spectra of the hydrogen atom.

1.4.4 Historical Background of Quantum Mechanics   Note: This topic is covered by the reading assigned beneath subunit 1.4.  Please review Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes for a narrative of the experimental work that led to quantum theory.

1.5 The Wave-Particle Duality  

  • Reading: Morningside College: Dave Slaven’s “Wave-Particle Duality: Light,” “Wave-Particle Duality: Electrons,” “The Meaning of the Wave,” and “From Many Waves, One” Link: Morningside College: Dave Slaven’s “Wave-Particle Duality: Light”, “Wave-Particle Duality: Electrons”, “The Meaning of the Wave”, and “From Many Waves, One” (HTML)
     
    Instructions: Please click on the links above, and read these four webpages.  While studying this resource, pay close attention to the mathematical model of a single wave and a wave packet, and understand the relationship among momentum, energy, and frequency in waves.  These resources provide a full overview of the wave-particle duality: how electrons behave like waves and how waves have “matter” properties.  Studying these resources should take approximately 2.5 hours to complete.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: YouTube: Adam Beatty’s “Wave Particle Duality” Link: YouTube: Adam Beatty's “Wave Particle Duality” (YouTube)
     
    Instructions: Please click on the link above, and watch the entire video.  This resource provides a recorded explanation of the wave-particle duality: how electrons behave like waves and how waves have “matter” properties.  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.

1.6 The de Broglie Wavelength  

  • Reading: University of California, Davis: UC Davis ChemWiki’s “De Broglie Wavelength” Link: University of California, Davis: UC Davis Chemwiki’s “De Broglie Wavelength” (HTML)

    Instructions: Clicking on the above link opens the resource webpage.  While reading this resource, repeat the mathematical derivation of the De Broglie equation.  This resource shows you the derivation of the De Broglie equation from Einstein’s equation and Plank’s equation.  Studying this resource should take approximately 0.50 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 006: The de Broglie Wavelength” Link: YouTube: Physics Academy’s “Quantum Mechanics 006: The de Broglie Wavelength” (YouTube)

    Instructions: By clicking on the above link to access a video showing the derivation of the De Broglie equation.  While watching the video, repeat the derivation on your own.  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 2” Link: The Saylor Foundation’s “Assessment 2” (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.