4 Matching Annotations
1. Dec 2023
2. tgvaughan.github.io tgvaughan.github.io
1. 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

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3. Feb 2023
1. | 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 real-valued solutions | self-adjoint linear operators on the state space<br>- some confusion may result when operators don't commute; there are usually no simple (real-valued) numerical solutions |

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5. docdrop.org docdrop.org
1. Principle (The Born rule). Given an observable O and two unit-norm states|ψ1〉 and |ψ2〉 that are eigenvectors of O with distinct eigenvalues λ1 and λ2O|ψ1〉 = λ1|ψ1〉, O|ψ2〉 = λ2|ψ2〉the complex linear combination statec1|ψ1〉 + c2|ψ2〉will not have a well-defined value for the observable O. If one attempts tomeasure this observable, one will get either λ1 or λ2, with probabilities|c21||c21| + |c22|and |c22||c21| + |c22|respectively.

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6. May 2015
7. dspace.mit.edu dspace.mit.edu
1. Solved Exams and Problems in advanced classical mechanics. Great Source!