Translation for "aikaderivaatta" to english

Aikaderivaatta

• the time derivative
• time derivative

Translation examples

time derivative

On myös mahdollista yhdistää Hamiltonin–Jacobin yhtälö ja ohjausyhtälö, jolloin saadaan näennäisesti Newtonin mekaniikkaa muistuttava liikeyhtälö: m d d t v → = − ∇ ( V + Q ) , {\displaystyle m\,{\frac {d}{dt}}\,{\vec {v}}=-\nabla (V+Q)\;,} missä hydrodynaaminen aikaderivaatta määritellään seuraavasti: d d t = ∂ ∂ t + v → ⋅ ∇ . {\displaystyle {\frac {d}{dt}}={\frac {\partial }{\partial t}}+{\vec {v}}\cdot \nabla \;.} Schrödingerin yhtälö monen kappaleen aaltofunktiolle ψ ( r → 1 , r → 2 , ⋯ , t ) {\displaystyle \psi ({\vec {r}}_{1},{\vec {r}}_{2},\cdots ,t)} on: i ℏ ∂ ψ ∂ t = ( − ℏ 2 2 ∑ i = 1 N ∇ i 2 m i + V ( r 1 , r 2 , ⋯ r N ) ) ψ {\displaystyle i\hbar {\frac {\partial \psi }{\partial t}}=\left(-{\frac {\hbar ^{2}}{2}}\sum _{i=1}^{N}{\frac {\nabla _{i}^{2}}{m_{i}}}+V(\mathbf {r} _{1},\mathbf {r} _{2},\cdots \mathbf {r} _{N})\right)\psi } Kompleksinen aaltofunktio voidaan esittää muodossa: ψ = ρ exp ⁡ ( i S ℏ ) {\displaystyle \psi ={\sqrt {\rho }}\;\exp \left({\frac {i\,S}{\hbar }}\right)} Pilottiaalto ohjaa hiukkasten liikettä.
One can also combine the modified Hamilton–Jacobi equation with the guidance equation to derive a quasi-Newtonian equation of motion m d d t v → = − ∇ ( V + Q ) , {\displaystyle m\,{\frac {d}{dt}}\,{\vec {v}}=-\nabla (V+Q)\;,} where the hydrodynamic time derivative is defined as d d t = ∂ ∂ t + v → ⋅ ∇ . {\displaystyle {\frac {d}{dt}}={\frac {\partial }{\partial t}}+{\vec {v}}\cdot \nabla \;.} The Schrödinger equation for the many-body wave function ψ ( r → 1 , r → 2 , ⋯ , t ) {\displaystyle \psi ({\vec {r}}_{1},{\vec {r}}_{2},\cdots ,t)} is given by i ℏ ∂ ψ ∂ t = ( − ℏ 2 2 ∑ i = 1 N ∇ i 2 m i + V ( r 1 , r 2 , ⋯ r N ) ) ψ {\displaystyle i\hbar {\frac {\partial \psi }{\partial t}}=\left(-{\frac {\hbar ^{2}}{2}}\sum _{i=1}^{N}{\frac {\nabla _{i}^{2}}{m_{i}}}+V(\mathbf {r} _{1},\mathbf {r} _{2},\cdots \mathbf {r} _{N})\right)\psi } The complex wave function can be represented as: ψ = ρ exp ⁡ ( i S ℏ ) {\displaystyle \psi ={\sqrt {\rho }}\;\exp \left({\frac {i\,S}{\hbar }}\right)} The pilot wave guides the motion of the particles.