4 Matching Annotations
- Dec 2023
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tgvaughan.github.io tgvaughan.github.io
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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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- Feb 2023
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www.youtube.com www.youtube.com
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| 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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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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- May 2015
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dspace.mit.edu dspace.mit.edu
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Solved Exams and Problems in advanced classical mechanics. Great Source!
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