While you pine away for your QUANTUM FIX this week,

a suggestion may be to

(A) Try solve for the eigenstates of

Morse oscillator

(the potential plotted in PROJECT 1 with ALPHA=0.1)

or more challenging ...

(B) Time-dependent stuff ....

(1)With your basis set code you now have the ability

to calculate the lowest 10 eigenstates of the quartic

oscillator with approximately 30 basis states.

Consider, for example the quartic system with beta = 5.

Let's look at a non-stationary initial state,

exp(-0.5*(x-1.)**2)

Firstly, using your numerical integration routine

(1) Expand this initial non-stationary state as a

linear combination of the quartic oscillator eigenstates

(2). For times from 0 to 5 units, calculate the evolution

of this initial wavepacket.

HINTS:!! If the initial wavepacket is a sum of the eigenstates

remember its evolution is then rather simple;

The expansion coefficients each get multiplied by a phase

factor!!

Show the evolution of the wavepacket at say, times = 0,1,2,3,4

by plotting the wavefunction abs(psi(x))**2 versus x for these times