Modern Physics  (comments to:     

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List of Modern Physics Problems
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For a start ...
derive the first eight Legendre polynomials in two different ways legendre
energy distribution of a light bulb using Planck's formula lhgtbulb
density plot of a p orbital shell pshell
And then ...
wave packets interacting with a potential barrier barrier
a fast charged particle gives energy to another charge as it races past (from E&M packet) particle
temperature dependance on wavelengths in Planck's formula plank
compare Rayleigh-Jeans and Planck radiation formulas rayplack
solution to Schrodinger's equation for a particle in a one-dimensional box schro
Derivation of the compton wavelength formula from energy and momentum comptn2

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