물리:포커-플랑크_방정식

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물리:포커-플랑크_방정식 [2026/03/10 12:43] – [마틴-시지아-로즈(Martin-Siggia-Rose, MSR) 범함수 형식론] admin물리:포커-플랑크_방정식 [2026/03/10 12:50] (current) – [포커-플랑크 방정식] admin
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 \begin{eqnarray*} \begin{eqnarray*}
 \rho(x, t+\Delta t) &=& \int dx' \int \frac{dk}{2\pi} \int \frac{d\Delta W}{\sqrt{2\pi \Delta t}} \exp\left\{ -ik \left[ x-x'-a(x') \Delta t-\Delta W \right] - \frac{(\Delta W)^2}{2\Delta t} \right\} \rho(x',t)\\ \rho(x, t+\Delta t) &=& \int dx' \int \frac{dk}{2\pi} \int \frac{d\Delta W}{\sqrt{2\pi \Delta t}} \exp\left\{ -ik \left[ x-x'-a(x') \Delta t-\Delta W \right] - \frac{(\Delta W)^2}{2\Delta t} \right\} \rho(x',t)\\
 +&=& \int dx' \int \frac{dk}{2\pi} \exp\left\{ -ik \left[ x-x'-a(x') \Delta t \right] - \frac{1}{2} \Delta t k^2 \right\} \rho(x',t)\\
 &=& \frac{1}{\sqrt{2\pi \Delta t}} \int dx' \exp\left\{- \frac{[x-x'-a(x')\Delta t]^2}{2\Delta t} \right\} \rho(x',t). &=& \frac{1}{\sqrt{2\pi \Delta t}} \int dx' \exp\left\{- \frac{[x-x'-a(x')\Delta t]^2}{2\Delta t} \right\} \rho(x',t).
 \end{eqnarray*} \end{eqnarray*}
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