Hearten
发表于 2025-3-26 23:14:33
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adequate-intake
发表于 2025-3-27 03:16:37
,The Hamilton–Jacobi Equation,We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2. coordinates (.., ..) to 2. constant values (.., ..), e.g., to the 2. initial values . at time . = 0. Then the problem would be solved, . = .(.., .., .), . = .(.., .., .).
WITH
发表于 2025-3-27 07:27:28
Action-Angle Variables,In the following we will assume that the Hamiltonian does not depend explicitly on time; .∕. = 0. Then we know that the characteristic function .(.., ..) is the generator of a canonical transformation to new constant momenta .. (all .. are ignorable), and the new Hamiltonian depends only on the ..: . = . = .(..).
JEER
发表于 2025-3-27 09:46:47
Superconvergent Perturbation Theory, KAM Theorem (Introduction),Here we are dealing with an especially fast converging perturbation series, which is of particular importance for the proof of the KAM theorem (cf. below).
Flustered
发表于 2025-3-27 15:17:55
Fundamental Principles of Quantum Mechanics,There are two alternative methods of quantizing a system:
CAND
发表于 2025-3-27 21:32:31
https://doi.org/10.1007/978-3-030-28003-1 ., ., are points in .-dimensional configuration space. Thus ..(.) describes the motion of the system, and . determines its velocity along the path in configuration space. The endpoints of the trajectory are given by ..(..) = .., and ..(..) = ...
掺和
发表于 2025-3-28 00:31:41
Maintaining Temporal Warehouse Models, translation . and .(..) = 0. Then the noninvariant part of the action, . is given by . and thus it immediately follows for the variation of . that . or . Here we recognize Newton’s law as nonconservation of the linear momentum: . Now it is straightforward to derive a corresponding law of nonconserv
MUTED
发表于 2025-3-28 02:22:43
Katalin Ternai,Szabina Fodor,Ildikó Szabóparticular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points . and . by ., then Jacobi’s princi
defile
发表于 2025-3-28 09:01:20
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DIS
发表于 2025-3-28 13:50:51
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