Recent content by limddavid

ok.. so i expanded that, and got ψ(x)+aψ'(x)+a^2*ψ''(x)/2!+ ... But the LHS gives me: e^(i*a*px)[ψ(x)]=e^(a*dψ/dx)=e^(-iak*ψ(x)), which is clearly not the left hand side. Am I interpreting the operator px wrong? This class is not a quantum dynamics class, so I'm having difficulty figuring...

Ok. so would the taylor series be: ψ(a+a)+ψ'(a+a)(x-a)+ψ''(a+a)*(x-a)^2/2!+... ? and maybe disregard the higher order terms O(3)? Or would it be ψ(a)+ψ'(a)*(x)+ψ''(a)*(x)^2/2!+... ? Either way, I'm not sure how I would prove that T(a) is the given exponential function..

Homework Statement A translation operator T(a) coverts ψ(x) to ψ(x+a), T(a)ψ(x) = ψ(x+a) In terms of the (quantum mechanical) linear momentum operator p_x = -id/dx, show that T(a) = exp(iap_x), that is, p_x is the generator of translations. Hint. Expand ψ(x+a) as a Taylor series...

Homework Statement With \vec{L} = -i\vec{r} x \nabla, verify the operator identities \nabla = \hat{r}\frac{\partial }{\partial \vec{r}}-i\frac{\vec{r}\times\vec{L}}{r^{2}} and \vec{r} \bigtriangledown ^2 - \bigtriangledown (1+\vec{r}\frac{\partial }{\partial \vec{r}})=i\bigtriangledown \times...

Ok.. I tried to root test, but I'm not sure how I can take the limsup of what I get: n^(u/n)/u

Homework Statement "Determine whether the following series converge: \sum_{n \geq 2} \frac{n^{ln (n)}}{ln(n)^{n}} and \sum_{n \geq 2} \frac{1}{(ln(n))^{ln(n)}} Homework Equations The convergence/divergence tests (EXCEPT INTEGRAL TEST): Ratio Dyadic Comparison P-test...