This cyclic ozone(O3) where bonds can be described by springs with strength 𝑘, and 𝑀 is the atomic mass
Posted: Fri May 06, 2022 6:52 am
This cyclic ozone(O3) where bonds can be described by
springs with strength 𝑘, and 𝑀 is the atomic mass of Oxygen.
1) Find the classical Lagrangian for this system, using the
positions of each atom {𝑥i} and the velocities of each
atom {𝑥̇i} as generalized coordinates. Assume the
vibrations can only occur along the axis of the molecule.
2) Use the Euler-Lagrange equations to find the normal
modes of the system(assuming a simple harmonic solution).
Have only real, positive frequencies.
3) Find the Hamiltonian of this system in terms of the atomic
momenta and the atomic positions.
springs with strength 𝑘, and 𝑀 is the atomic mass of Oxygen.
- This Cyclic Ozone O3 Where Bonds Can Be Described By Springs With Strength K And M Is The Atomic Mass Of Oxygen 1 Fi 1 (10.81 KiB) Viewed 47 times
positions of each atom {𝑥i} and the velocities of each
atom {𝑥̇i} as generalized coordinates. Assume the
vibrations can only occur along the axis of the molecule.
2) Use the Euler-Lagrange equations to find the normal
modes of the system(assuming a simple harmonic solution).
Have only real, positive frequencies.
3) Find the Hamiltonian of this system in terms of the atomic
momenta and the atomic positions.