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A turning point of a differentiable function is a point at which the derivative has an isolated zero and changes sign at the point. [2] A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). A turning point is thus a stationary point, but not all stationary points are turning points.
A stationary state is called stationary because the system remains in the same state as time elapses, in every observable way. For a single-particle Hamiltonian , this means that the particle has a constant probability distribution for its position, its velocity, its spin , etc. [ 1 ] (This is true assuming the particle's environment is also ...
Potential energy surfaces are commonly shown as three-dimensional graphs, but they can also be represented by two-dimensional graphs, in which the advancement of the reaction is plotted by the use of isoenergetic lines. The collinear system H + H 2 is a simple reaction that allows a two-dimension PES to be plotted in an easy and understandable way.
The x-coordinates of the red circles are stationary points; the blue squares are inflection points. In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. [1]
English: Graph of () = + and shows stationary points (red circles) and inflection points (blue squares). The stationary points in this graph are all relative maxima or relative minima. The stationary points in this graph are all relative maxima or relative minima.
Maxwell's equations can be derived as conditions of stationary action. The Einstein equation utilizes the Einstein–Hilbert action as constrained by a variational principle. The trajectory (path in spacetime) of a body in a gravitational field can be found using the action principle. For a free falling body, this trajectory is a geodesic.
Stationary distribution may refer to: Discrete-time Markov chain § Stationary distributions and continuous-time Markov chain § Stationary distribution , a special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal distribution of all states at any time will always be the stationary ...
Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative , if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum.