Problem Set 5 for Quantum Chemistry Course (CHEM482) - Solutions and Calculations - Prof. , Assignments of Physical Chemistry

Download Problem Set 5 for Quantum Chemistry Course (CHEM482) - Solutions and Calculations - Prof. and more Assignments Physical Chemistry in PDF only on Docsity! Problem set 5 (8 points) Due: Oct 13 CHEM482: QUANTUM CHEMISTRY 1. [3 point] By substituting in the Schrödinger equation for rotation in three dimensions, show that the rotational wavefunction 3 cos2 θ − 1 is an eigenfunction of the Hamiltonian. Determine the energy eigen- value which corresponds to this wavefunction. Normalize the wave- function. 2. [1 point] Calculate the average momentum, 〈L̂z〉, for particle in a ring having wavefunction 1√ 2π e−3iφ 3. [3 point] Give a simple reason why (2 + q− 3q2)e−q2/2 can not be a satisfactory wavefunction for the harmonic oscillator. You should be able to answer by inspection, (almost) without calculations, and without reference to tabulations. 4. [1 point] Demonstrate by direct integration that two wavefunctions for particle in a ring are orthogonal to each other if they belong to different energies. 1