Difference between revisions of "PCh7 lec3"
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| + | As we move forward to discuss the particle on a ring, ie. rotation in 1D, the biggest change that happens is that we need to change the coordinate system from cartesian coordinates to spherical polar coordinates (SPC). Have a look at the following video to help understand this conversion (''reminder: document your work, ie. take some notes''). | ||
| + | |||
| + | :[https://youtu.be/w79nZGzWMyI Deriving Spherical Coordinates (For Physics/Chemistry Majors) 5:03 min] | ||
| + | : See Fig 2.5 (Engel) for SPC diagram. | ||
| + | |||
| + | ===Particle on a Ring=== | ||
| + | Have a look at the following video: | ||
| + | :[https://youtu.be/N3CErWITjJo Particle-on-a-Ring: Theory and Interpretation (10:55 min)] | ||
| + | |||
| + | Note: | ||
| + | :- there appears to be two wavefunction (clockwise rotation and counter-clockwise rotation) eq. 7.12, but instead of thinking about two solutions, we move the negative value into the integer m<sub>l</sub>, so the values for ml = 0, ±1, ±2, ±3, etc. | ||
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| + | Add the operator, wavefunction, and energy to your table. | ||
| + | |||
| + | Please complete/write out Ex. Problem 7.4 (page 114), Determine/verify the normalization constant for the wavefunction. | ||
| + | |||
| + | '''End of Lecture 3.''' | ||
Latest revision as of 21:51, 25 April 2020
(3/23/20, bes)
As we move forward to discuss the particle on a ring, ie. rotation in 1D, the biggest change that happens is that we need to change the coordinate system from cartesian coordinates to spherical polar coordinates (SPC). Have a look at the following video to help understand this conversion (reminder: document your work, ie. take some notes).
- Deriving Spherical Coordinates (For Physics/Chemistry Majors) 5:03 min
- See Fig 2.5 (Engel) for SPC diagram.
Particle on a Ring
Have a look at the following video:
Note:
- - there appears to be two wavefunction (clockwise rotation and counter-clockwise rotation) eq. 7.12, but instead of thinking about two solutions, we move the negative value into the integer ml, so the values for ml = 0, ±1, ±2, ±3, etc.
Add the operator, wavefunction, and energy to your table.
Please complete/write out Ex. Problem 7.4 (page 114), Determine/verify the normalization constant for the wavefunction.
End of Lecture 3.