[OZpharmer]

I am a graduate student pursuing a Master's degree in chemistry and I am struggling through a mandatory quantum chemistry course(I did not take any physical chemistry course during my undergrad years, so this area is very new to me).

I would like to get some help in these questions:


1) When e^(d/dx) = 1 + (d/dx) + (1/2!)(d²/dx²) + (1/3!)(d³/dx³) + ...+ (1/n!)(d²/dxⁿ),

Show that e^(d/dx) = T₁(hat operator),
where T₁(hat operator)[f(x)] = f(x+1)


2) Find the eigenfunctions and eigenvalues of ∫ dx

Thank you.