I'm currently using David J. Griffiths 'Introduction to Quantum Mechanics' to teach myself quantum mechanics and I had a quick question about the way he factors the Hamiltonian into the raising and lowering operators for the potential V(x)=(1/2)kx²
On page 42 he writes the Hamiltonian as...
okay so I get that part, but in the same line (within 1.25) he writes:
iℏ/2m(ψ*∂²/∂x²[ψ]-∂²/∂x²[ψ*]ψ) = iℏ/2m(∂/∂x)(ψ*∂/∂x[ψ]-∂/∂x[ψ*]ψ) [1.25]
how did he factor out the partial derivative with respect to x on the RHS? To my knowledge, if you apply the partial derivative on the RHS then I...
I'm having trouble understanding what David Griffith did in equation [1.25]. In this section he's trying to prove that psi stays normalized and I'm following him from [1.21] to [1.25] and where I'm getting stuck is understanding how:
∂/∂t|ψ|^2= i\hbar/2m(ψ*∂²/∂x²[ψ]-∂²/∂x²[ψ*]ψ)...