PCh7 lec3

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(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:

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 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.