Quantum Mechanics for Rotational Spectroscopy
This video covers the fundamental quantum mechanics necessary to fully explain the rovibrational spectrum of HCl (time stamps below). Specifically, we build up from the quantum rigid rotor and quantum harmonic oscillator, as well as calculating the transition dipole moment using spherical harmonic wavefunctions.
This video is part of my Quantum Mechanics for Physical Chemistry playlist, so the prerequisite material can be found here: • Quantum Mechanics
0:00 - Introduction
1:05 - Motivations behind spectroscopy in general
4:20 - The Hamiltonian
5:33 - Quantum “toy models” used to explain molecular motions
8:29 - Statement of the gross selection rule
12:22 - Dipoles responding to oscillating electric fields
15:18 - Rotating dipoles producing oscillating electric fields
18:03 - Review of wavefunctions and the Kronecker delta
19:22 - Expectation values of observables
22:00 - The transition dipole integral
23:45 - Bra-ket notation
24:53 - Building from dipole operator to transition dipole operator
27:18 - Deriving the gross selection rule from the transition dipole operator
28:36 - Begin deriving other selection rules
29:17 - Even and odd functions
34:44 - Generalizing even and odd to parity in 3D
40:12 - Deriving selection rules from wavefunction parity and the transition dipole operator
47:08 - The effect of photon spin angular momentum on selection rules
49:46 - Rovibrational spectra using FT-IR
52:16 - Explaining the theoretical rovibrational spectrum of a linear rotor with harmonic coupling
1:02:56 - Explaining the experimental rovibrational spectrum of a HCl
1:19:04 - Thank you for watching