The Hermite polynomials Hn(x) are special functions that are extremely im- portant in quantum mechanics. The Hn(x) may be defined by: P(x, h) = exp(2rh – h²) = H,(x)h". n=0 Show that 2x + 2h 0. %3D...

Extracted text: The Hermite polynomials Hn(x) are special functions that are extremely im- portant in quantum mechanics. The Hn(x) may be defined by: P(x, h) = exp(2rh – h²) = H,(x)h". n=0 Show that 2x + 2h 0. %3D and hence H" («) — 2 Н, (х) + 2nH, (2) — 0.