In \sum_{i=1}^{4}((x_{i}-x_{i-1})^2+k_ix_i) you have x_0 term, so I assume that indices are cyclic and x_0=x_4. You have to expand \sum_{i=1}^{4}(x_{i}-x_{i-1})^2 and then write it as (Einstein convention used) A_{ij}x_i x_j. Notice that as x_i x_j=x_j x_i, matrix \mathbb{A} is not unique...
Hello. I've an integral:
\int_{-\infty}^{0}x\exp(-x^2)H_n(x-a)H_n(x+a)dx
Of course for any given n it can be calculated, but I'm interested if there is some general formula for arbitrary n. Could someone with access type that into Mathematica? In case that there exists general formula, idea how...
Hello!
I was reading a paper on formulation of QM in phase space (https://arxiv.org/abs/physics/0405029) and I have some doubts related to chapter 5. It seems to me that there is a transformation to modified polar coordinates (instead of radius there is u which is square of radius multiplied by...