From 15c24e0fd1dc243023dd35ba21138709ada32086 Mon Sep 17 00:00:00 2001 From: Michael Wimmer <m.t.wimmer@tudelft.nl> Date: Sun, 12 Sep 2021 20:54:09 +0000 Subject: [PATCH] write down initial and boundary conditions separately --- src/8_differential_equations_2.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md index 35b5cde..1814b10 100644 --- a/src/8_differential_equations_2.md +++ b/src/8_differential_equations_2.md @@ -271,8 +271,9 @@ arise from the time derivative and likewise at least one from the spatial derivative. For the Schrödinger equation, we could supply the initial conditions - -$$\psi(x,0)=\psi_0(x) \& \psi(0,t) = \psi(L, t) = 0 \text{for all $t$}.$$ +$$\psi(x,0)=\psi_0(x)$$ +together with the boundary conditions +$$\psi(0,t) = \psi(L, t) = 0 \text{for all $t$}.$$ This particular set of boundary conditions corresponds to a particle in a box, a situation which is used as the base model for many derivations in quantum -- GitLab