I am responsible for teaching the solid state physics exercise class in this semester (Winter Semester 2022/2023). The first exercise was deriving the motion expression of simple and coupled harmonic oscillators and their eigenfrequencies.
The general idea is firstly constructing the mathematical equations using Newton’s second law and Hooke’s law and then solving the second order differential equations.
The eigenfrequency w=sqrt(d/m) of a simple harmonic oscillator will be obtained. The expression is helpful to understand the isotopic substitution experiments, for example, why the vibrational frequency of -OH is about 1.414 times higher than the vibrational frequency of -OD.
Regarding the coupled oscillator, there are two eigenfrequencies w1=sqrt(d/m), w2=sqrt[(d+2δ)/m]. w1 is the eigenfrequency under symmetric stretch, where the two particles moves consistently in the same direction with the same frequency, and the interaction between them remains unchanged during the motion. w2 is the eigenfrequency under asymmetric stretch, where the interaction between two particles moves in the opposite direction, and the interaction between them needs to be considered. These are very helpful to understand the different vibrational modes in the molecules.
Zhipeng Huang
Senior Research Associate
My research interests include ultrafast electron/X-ray diffraction, ultrafast spectroscopies, non-linear optics, (ultrafast) chemical and physical dynamics at surface or interface, etc.