9 Matching Annotations
  1. Mar 2023
  2. 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 |

    1. Principle (Observables). States for which the value of an observable can becharacterized by a well-defined number are the states that are eigenvectors forthe corresponding self-adjoint operator. The value of the observable in such astate will be a real number, the eigenvalue of the operator.

      What does he mean precisely by "principle"?

    2. Axiom (Dynamics). There is a distinguished quantum observable, the Hamil-tonian H. Time evolution of states |ψ(t)〉 ∈ H is given by the Schr ̈odingerequationi~ ddt |ψ(t)〉 = H|ψ(t)〉 (1.1)
    3. Axiom (Quantum observables). The observables of a quantum mechanical sys-tem are given by self-adjoint linear operators on H.
  3. Jan 2019
    1. function sequenceSubscriber(observer) { // synchronously deliver 1, 2, and 3, then complete observer.next(1); observer.next(2); observer.next(3); observer.complete();  // unsubscribe function doesn't need to do anything in this // because values are delivered synchronously return {unsubscribe() {}};} // Create a new Observable that will deliver the above sequenceconst sequence = new Observable(sequenceSubscriber); 

      key point as this is a 'classical' implementation of the Observable.

  4. Dec 2018
    1. As a publisher, you create an Observable instance that defines a subscriber function

      this is how you create an observable others can observe and get updates from

  5. Oct 2018