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Physics
The Schrödinger equation
The Schrödinger equation, \(i \hbar \frac{\partial \Psi}{\partial t} = \hat H \Psi\), is a partial differential equation for the wave function \(\Psi\) of quantum mechanics.
Physics
The wave equation
The wave equation, \(\frac{\partial^2u}{\partial t^2}= c^2\nabla^2 u\), relates how \(u\) varies with time and with the spatial coordinates as a wave propagates with speed \(c\).
Mathematics
The definition of conditional probability
The conditional probability that an event \(A\) occurs given the occurrence of another event \(B\) is \(P(A|B) = \frac{P(A \cap B)}{P(B)}\).