••• Problem 1 estimates the time At for collapse of a classical hydrogen atom, making the...

••• Problem 1 estimates the time At for collapse of a classical hydrogen atom, making the approximation that it shrinks at a constant rate. Calculate Δt without making that approximation, as follows: Use Eq. (11.49) to find dr/dt, the rate at which the or? shrinks, as a function of r, and find the time for this classical atom to collapse entirely, by evaluating

Problem 1

• The Hamiltonian operator is often described as a linear operator because it has the linear property thai H[Aψ(x) + Bϕ(x)] = AHψ(x) + BHϕ(x) for any two functions ψ(x) and ϕ(x) and any two constant numbers A and B. Prove that the one-dimensional Hamiltonian (11.11) is linear.