Ive got an equation(schrodingers equation for an anharmonic potential oscillator) -d^2(wavefunction) + (a*x^2+b*x^N)wavefunction = E (wavefunction) dx^2 Id like to construct the wavefunction for different values of E and using some boundry conditions.. (i know what the value of the wavefunction is at x = 0). The values of a,b and N are also known. Anyone got any ideas how i would go about constructing the wavefunction ? [edited by - quant on March 21, 2003 5:38:43 PM]

Well, the first answer that comes to mind is C * e ^ (wx) (or Csin(wx), but I don''t think that they will work. I have no idea how to deal with your x^N. If that''s Schrodinger''s equation, I''m sure that you can find plenty of answers on Google.

Good luck,

Cédric

Had another idea:

e ^ f(x)

This will give you, after using it in your ODE:

-f''''(x)² - f''''(x) + a*x² + b*x^N - E = 0

This is a quadratic equation in f''''. You can solve for f'''' and get an equation that must be integrated twice... Wolfram''s integrator gave me some weird results for the first integral, so I don''t know if it can be done. It could be done numerically, though.

Cédric