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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 ...
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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} ...
