2
votes
0answers
27 views

Some question about symplectic transformation

I read Arnold's book Mathematical Methods of Classical Mechanics and come across with three problems in page 229. 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues of a ...
5
votes
2answers
141 views

Examples of singularities in classical physics

I am a math teacher and I have to teach a topic called "Bruchterme" and "Bruchgleichungen" in german (I don't know the english word for it). For example $$ \frac{x^2 - 3}{(x - 2)x^2} + \frac{4}{x} + ...
0
votes
1answer
193 views

Solution of a partial differential heat equation with derivative and boundary conditions

I want to solve the following partial different equation. Find $u(x, t)$, satisfying $u_t = u_{xx}$ , $u(x, 0) = x − x^2$ , $u(0, t) = T_0$ , $u_x (1, t) = 0$ and $|u|$ is bounded. Using separation ...
2
votes
0answers
135 views

Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use $$\sum_{n} ...