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Lecture 17: Quantum States and Spin
March 31, 2026
Reading Assignment
- Read: Supplementary Reading Ch 5
Objectives
- (Continuing objective) Describe applications of the concepts of quantum mechanics to everyday “real-life” situations.
- Express the state of a quantum system in terms of state vectors. Explain what is meant by the state being “normalized.”
- Explain what is meant by a measurement on a quantum state and the meaning of “collapse of the state.” Given a superposition state, determine the possible results of a measurement of, for example, energy or a spin component and compute the probabilities of obtaining various possible results.
- Describe aspects of quantum mechanical “spin” that can't be explained classically.
- Given a spin state written in one basis, write the same spin state in a different basis. For example, given a spin $|\text{$\psi$}\rangle$ state in the $|\text{$\pm z$}\rangle$ basis, be able to express the same state in the $|\text{$\pm x$}\rangle$ basis.
Homework
- Wednesday's Assigned Problems:
A74; Supp CH 5: 1, 3, 5, 9, 10, 11, 14, 17, 20
- Monday's Hand-In Problems from Lecture 17:
Supp CH 5: 4, 12, 13, 15, 19
Note: this is only the first half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 6; CT2 - 1; CT3 - 1; CT4 - 4; CT5 - 3
- Whole Brain Atlas -- MRI scans of the brain.
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.- Video example: Dealing with a superposition state. NOTE: when this example was made (a few years ago), we didn't take into account the possibility of complex coefficients (i.e., with ``$i$`'' in them). So, in addition to $\sqrt{3/4}$ for $b$, $b$ could also be $-\sqrt{3/4}$, $i\sqrt{3/4}$, or $-i\sqrt{3/4}$.
- Video Example: Another example with this state stuff. As with the second example above, there are actually a few different possibilities for the constant a.
- Simple example of finding resonant frequency to flip a proton (NMR example).
- Video Example: Magnetic Resonance. This one also looks at spatial variation, something that can be used in MRI devices to probe particular parts of a patient's body.
Pre-Class Entertainment
- The Times They are a-Changin' - Bob Dylan
- I Feel the Earth Move - Carole King
- Banana Pancakes - Jack Johnson
- What's So Funny 'Bout Peace, Love, & Understanding - Elvis Costello
- See Saw - Aretha Franklin