conjugated momentum造句

• Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate momentum.
• This conjugate momentum is the magnitude " L " of the angular momentum, as shown by the Hamiltonian equation of motion for ?
• Since the azimuthal angle ? does not appear in the Hamiltonian, its conjugate momentum " p " ? is a constant of the motion.
• In the connection representation the configuration variable is A _ a ^ i and its conjugate momentum is the ( densitized ) triad \ tilde { E } _ i ^ a.
• It turns out that \ tilde { E } ^ a _ i is the conjugate momentum of A _ a ^ i, and together these form Ashtekar's new variables.
• Taking the partial time derivative of the definition of the Hamiltonian density above, and using the chain rule for implicit differentiation and the definition of the conjugate momentum field, gives the continuity equation:
• The densitized drei-bein is the conjugate momentum variable of this three-dimensional SU ( 2 ) gauge field ( or connection ) A ^ j _ b, in that it satisfies the Poisson bracket relation
• We define the conjugate momentum of the scalar field with the usual \ tilde { \ pi } = \ delta L / \ delta \ dot { \ varphi }, the Hamiltonian can be rewritten as,
• It can be shown that six Einstein equations describing time evolution ( really a gauge transformation ) can be obtained by calculating the Poisson brackets of the three-metric and its conjugate momentum with a linear combination of the spatial diffeomorphism and Hamiltonian constraint.
• As in Hamiltonian mechanics where every generalized coordinate has a corresponding generalized momentum, the field has a "'conjugate momentum field "', defined as the partial derivative of the Lagrangian density with respect to the time derivative of the field,
• For example, if we use polar coordinates " t, r, ? " to describe the planar motion of a particle, and if " L " does not depend on " ? ", the conjugate momentum is the conserved angular momentum.
• In Ashtekar formulation the gauge field A _ a ^ i ( x ) is the configuration variable ( the configuration variable being analogous to q in ordinary mechanics ) and its conjugate momentum is the ( densitized ) triad ( electrical field ) \ tilde { E } ^ a _ i ( x ).
• In the ADM formulation of general relativity one splits spacetime into spatial slices and time, the basic variables are taken to be the induced metric, q _ { ab } ( x ), on the spatial slice ( the metric induced on the spatial slice by the spacetime metric ), and its conjugate momentum variable related to the extrinsic curvature, K ^ { ab } ( x ), ( this tells us how the spatial slice curves with respect to spacetime and is a measure of how the induced metric evolves in time ).