5 15 Points Consider The Vibrations Of Molecular Bond I E C 0 Symmetric Stretching Of Carbon Dioxide Co2 Which Ca 1 (30.08 KiB) Viewed 51 times
5 15 Points Consider The Vibrations Of Molecular Bond I E C 0 Symmetric Stretching Of Carbon Dioxide Co2 Which Ca 2 (9.6 KiB) Viewed 51 times
5. (15 points) Consider the vibrations of molecular bond, i.e., C=0 symmetric stretching of carbon dioxide CO2, which can be modelled as a one-dimensional harmonic oscillator (HO) via the Hamilton function p2 1 H= +2 2m mox where p and x are the momentum and position, respectively. The typical frequency of the C=0 bond vibration is o = 1480cm. Knowing (Ap) = (p?) - (p) and (AxP) = (x?) - (x)?, one has the inequalities (a?) (Aa?) where Aa is the variance of quantity a. (a) State the Heisenberg's uncertainty relation for momentum and position, and its interpretation; (6) The mean energy of HO yields the inequality =
(p2) (Ap), 1 = +) + moʻ(AxP), 2m 2m please use the uncertainty relation to estimate the lower bound of the energy of the C=O bond vibration (H) = vent 3 mo?(8?) 2
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