PHYS-251 Intro to Quantum Mech I
III4 The Hydrogen Atom
1.
NEBRASKA WESLEYAN UNIVERSITY
SPRING 2012 – 2013
DUE: FRI 14 APR 2013
Create an animation (a “CAT scan”) of the n = 3, l = 2, m = 0 stationary state of the wave function for the electron bound
to a proton to form the H atom. Send the movie to me via email. Answer the following:
a) Does this wave function have an imaginary part? Why or why not?
b) At the y = 0 plane position, why is the real part positive in some places and negative in others (creating nodal curves
similar to those on a vibrating drumhead)? What functions and function values account for these values?
c) Is the probability density function a dumbbell or a donut?
2.
Create an animation (a “CAT scan”) of the n = 3, l = 2, m = 2 stationary state of the wave function for the electron bound
to a proton to form the H atom. Send the movie to me via email. Answer the following:
a) Does this wave function have an imaginary part? Why or why not?
b) Is the probability density function a dumbbell or a donut?
3.
What is a “p orbital?” Try creating a wave function that combines the radial factor with the following linear combination
of spherical harmonics: (𝑌1 −1 − 𝑌11 )⁄√2, 𝑖(𝑌1 −1 + 𝑌11 )⁄√2. Note that these are l = 1 states, but that m would be
indeterminate. Produce animations showing the wave function and probability density for these. Use n = 2.
a) Do these wave functions have imaginary parts? Why or why not?
b) Use a chemistry book or online resource to look at the probability density for a p orbital. Do these have the correct
appearance?
c) What spherical harmonic is a pz orbital?
DEAN SIEGLAFF
Created: 08 APR 2013
Modified:
1 of 1