Issued Wed, Oct 9 Due Wed, Oct 16

(Required reading for this week: Start Gas. Ch. 6

There are HINTS for this homework!

1a) Gas #5-9, but just do it for the two lowest eigenfunctions. (Don't forget to normalize)

b) What are the allowed energies of a "half-harmonic oscillator", where

(I.e., it's a spring which stretches but doesn't compress). No real calculation is required, just think!

2) Gas #5-14

3) Find the eigenfunctions, u(x), of H in the potential

(Don't bother to normalize them). Find the allowed energies (graphical solutions are o.k.) How do the energies compare with the corresponding energies for the well without the delta function in the middle? Sketch the first few eigenfunctions (up to n=3)

4) Gas #5-8

5) Consider an electron in a diatomic potential, modeled as a double delta function, ,

with a=1 Angstrom, and alpha = 8 eV A.

Find the allowed energies for the (bound) electron, and sketch the wave functions. Find the oscillation frequency, ,

Correction! I got the factor of 2 Pi upside down there, but I can't change the gif file. Sorry.

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