Friday, June 11, 2010

Quantum Soccer - Technical Notes

"The energy eigenfunctions of Schrödinger's equation for a two-dimensional square-well potential with infinitely high walls are:
φn,p(x,y,t) = (2/√LM) sin(nπx/L) sin(pπy/M) exp(–2πiEn,pt/h) (1)

where L and M are the dimensions of the well in the x- and y-directions (x and y being zero at one of the corners of the well), n and p are integers greater than or equal to 1, specifying the number of half-wavelengths that fit across the well in each direction, h is Planck's constant, and En,p is the energy of the eigenfunction, given by:
En,p = (h2/8m)((n/L)2 + (p/M)2)"

5 out of 5

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