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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.
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Ground state for a double well potential (Schrödinger)
Consider $V(x)$ a one dimensional polynomial, confining, symmetric double well potential i.e.
$V(x)=V(-x)$ for all $x\in\mathbb{R}$
$\displaystyle \lim_{x\to\pm\infty} V(x)=+\infty$
$V(x)\in \mathb …