# Method of steepest descent for a quartic oscillator

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1. Nov 4, 2015

2. Nov 9, 2015

### DrDu

in i and ii you have obtained a saddle point, but the directions in which the saddle will fall off (= steepest decent) will be different for the two cases lambda<0 and lambda >0. I.e. $F(z)\approx F(z_0)+F''(z_0)(z-z_0)^2/2$. If $F''(z_0)<0$, then the path of steepest descents will be for real z-z_0.