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Lecture 16: Quantized Energies and Spectra
March 26, 2026
Reading Assignment
- Read: Supplementary Reading Ch 4
Objectives
- (Continuing objective) Describe applications of the concepts of quantum mechanics to everyday “real-life” situations.
- For a particle in an infinite square well potential, draw the allowed wavefunctions \(\psi_n\) and express them mathematically. From the wavefunction, use Schrödinger's equation to calculate the corresponding energies \(E_n\).
- Describe and plot wavefunctions for a finite square well potential. Discuss the significance of a non-zero wavefunction in regions where \(E < U\). Use these ideas to explain quantum mechanical tunneling.
- Explain the band structure that typically describes quantum energy levels in extended systems.
- Relate the emitted or absorbed photon energies, wavelengths and frequencies to the energy levels of various systems. Explain fluorescent and phosphorescent behavior.
Homework
- Friday's Assigned Problems:
Supp CH 4: 1, 2, 4, 6, 9, 10, 12, 13, 14, 16
- Monday's Hand-In Problems from Lecture 16:
Supp CH 4: 3, 11, 15, 17, 18
Note: this is only the second half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 1, 2, 3; CT2 - 1, 5; CT3 - 3; CT4 - 1
- Simulation showing the wavefunctions and energy levels for the infinite square well.
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Long Lensoo example of particle in box, asking both for energy of a state and for probabilities of finding the electron in different regions. (This is a 10-minute video.)
- Lensoo Example showing how to work with absorption and emission processes, using a particle-in-box system. NOTE: Part (a) has a mathematical error -- the 8 in the denominator at the end of the problem shouldn't be there.
- Video example of light emitted from a transition. (This one uses the result for the energy levels of Hydrogen, which we haven't covered yet, but the equation for En is given, so this problem can be done with what you know from today's lecture.)
Pre-Class Entertainment
- Dire Wolf - The Grateful Dead
- Hold On, I'm Comin' - Sam & Dave
- What Would You Say - Dave Matthews Band
- All I Wanna Do - Sheryl Crow
- Late In the Evening - Paul Simon