Quantum chem 3

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Quantum chem 4

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Quantum chem 5

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Quantum chem 6

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Quantum chem 7

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Wavefunction

1.) A particle of mass m is confined to a one-dimensional potential well with infinite potential walls. The well extends from 0≤ x ≤ a. At time t = 0, the normalized wavefunction is Ψ(x, t=0) = (8/5a)1/2 [ 1 + cos (πx/a)] sin (πx/a) What is the wavefunction at a later time t = t0? (Hint: A ...continues

Energy Eigenfunctions of a particle

2.) Find for the first three energy eigenfunctions of a particle in an infinite dimensional well. (Hint: You might want to use the energy eigenvalues to avoid a lot of detailed calculations.)

Tunneling in Chemistry

4.) Find two examples of tunneling in chemistry from the literature. Explain where quantum mechanical tunneling is involved and reference the literature source.

Commutator of Wave Function

5.) Find the commutator of [x , d/dx ] for the wave function Ψ(x). See attached file for full problem description.

18-O and 16-O Isotope Effects in Infrared Spectroscopy. Predicting Absorption Frequencies.

The Pt compound below shows an infrared band at 822 cm-1 that has been attributed to the O-O stretching mode. This is the mode where the O atoms move away from each other and the Pt-O stretching is not significant. If you approximate the O-O unit as a harmonic oscillator, where would you expect the 18-O compound to absorb? k ...continues