Computational Physics - Department of Physics

536 16 Improved Monte Carlo Approaches to Systems of Fermions

H 4 (x) = 16 x^4 − 48 x^2 + 12.

They fulfil the orthogonality relation
∫∞
−∞

e−x

2

Hn(x)^2 dx= 2 nn!

√

π,

and the recursion relation
Hn+ 1 (x) = 2 xHn(x)− 2 nHn− 1 (x).