Homework 2 Part 2

Homework 2 Part 2 - Homework 2 Part 2 st(Due Feb 1 1 You have seen that linear combinations of time-independent orbitals can be combined via the

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Homework 2 Part 2 (Due Feb 1 st ) 1. You have seen that linear combinations of time-independent orbitals can be combined via the LCAO theory. We will now show that this also applies to time-dependent wavefunctions. Given that two wavefunctions, g m and g n , are orthonormal and stationary states with respect to the time-dependent Hamiltonian, show that ΨG±, ²³ = ´ µ g µ G±³¶ ·¸¹ º »/ℏ + ´ ¼ g ¼ G±³¶ ·¸¹ ½ »/ℏ satisfies the time-dependent Schrodinger equation. 2. Calculate the ΔE for a transition between the ν=0 b ν=1 state, for a: a. Harmonic oscillator obeying Hooke’s law b. Morse Potential 3. Determine the total degrees of freedom for each molecule below, as well its translational, rotational, and vibrational degrees of freedom. a. C 6 H 6 b. Formaldehyde c. CH 3 Cl 4. Describe the normal modes of vibration of SO 2 and CS 2 . Which are Raman active and which are infrared active? 5.
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This document was uploaded on 01/03/2012.

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Homework 2 Part 2 - Homework 2 Part 2 st(Due Feb 1 1 You have seen that linear combinations of time-independent orbitals can be combined via the

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