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 Dec 2023

tgvaughan.github.io tgvaughan.github.io

The dimension of the configuration space is the smallest number of parameters that have to be given to completely specify a configuration. The dimension of the configuration space is also called the number of degrees of freedom of the system.4
Definition of degrees of freedom of a system

 Feb 2023

www.youtube.com www.youtube.com

 physics/mathematics  Classical Physics  Quantum Mechanics <br /> <br />  State Space  fields satisfying equations of laws<br> the state is given by a point in the space  vector in a complex vector space with a Hermitian inner product (wavefunctions) <br />  Observables  functions of fields<br> usually differential equations with realvalued solutions  selfadjoint linear operators on the state space<br> some confusion may result when operators don't commute; there are usually no simple (realvalued) numerical solutions 



Principle (The Born rule). Given an observable O and two unitnorm statesψ1〉 and ψ2〉 that are eigenvectors of O with distinct eigenvalues λ1 and λ2Oψ1〉 = λ1ψ1〉, Oψ2〉 = λ2ψ2〉the complex linear combination statec1ψ1〉 + c2ψ2〉will not have a welldefined value for the observable O. If one attempts tomeasure this observable, one will get either λ1 or λ2, with probabilitiesc21c21 + c22and c22c21 + c22respectively.

 May 2015

dspace.mit.edu dspace.mit.edu

Solved Exams and Problems in advanced classical mechanics. Great Source!
