Recent content by jbay9009

Homework Statement A particle, mass m propagates freely in a box, length L. The energy states are: ϕ_n(x) = (2/L)^(1/2)sin(n∏x/L) and energies E_n = n^2∏^2/(2mL^2) at time t=0 the system is in state ϕ_1 and the perturbation V=kx is applied (k constant) and turned off at t=T...

Thanks, that seems to have pointed my along the right track. The y in b) was a typo but I suppose I could include it all the way through for the most general case. I think I can do it ok now, I end up with f(x)|inf - ∫(-inf to inf) ∂/∂x f(x) dx = f(x)|inf - f(x)|inf + f(x)|0 = f(0) as...

Thanks for your reply My current solutions are now: (a) I am given that ∫(-inf to inf) δ(x-y)f(x)=f(y) I changed y→a and said that f(x)→x-b so that this reads ∫(-inf to inf) δ(x-a)δ(x-b)=δ(a-b) as required (c) ∫(-inf to inf) δ(x) f(θ(x))dx = ∫(-inf to inf) ∂/∂x θ(x) f(θ(x))dx...

Homework Statement (a) Show that that δ(a-b)=∫δ(x-a)δ(x-b)dx (b) Show that ∂/∂x θ(x) = δ(x) where θ(x) is the heaviside step function (0 for x<0, 1 for x>0) (c) Show that ∫(-inf to inf) δ(x) f(θ(x))dx=∫(0 to 1) f(y)dy Homework Equations The definition of the delta function...