Vibrational spectroscopy
The quantum harmonic oscillator
Orthogonality of the wavefunctions of the quantum harmonic oscillator
Recurrence relations of the Hermite polynomials
Taylor series of single-variable and multi-variable functions
Generating function and Rodrigues’ formula for the Hermite polynomials
Normalisation constant for the wavefunctions of the quantum harmonic oscillator
Vibration of diatomic molecules
The Born-Oppenheimer approximation
Nuclear motion in diatomic molecules
Vibration of polyatomic molecules
Vibrational selection rules for molecules
Fourier-transform infrared spectroscopy