born's rule Definition and 12 Threads

The Born rule (also called Born's rule) is a postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of finding a system in a given state, when measured, is proportional to the square of the amplitude of the system's wavefunction at that state. It was formulated by German physicist Max Born in 1926.

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  1. M

    I Measurement of a superposition and Born's rule

    Let be a superposition ##|\psi\rangle=\sum_j a_j|j\rangle## with one amplitude ##a_x## much greater than the others, where ##x## is not known. For example, ##|\psi\rangle## may result from the quantum Fourier transform of a periodic wave function with an unknown period. I expect a measurement of...
  2. A. Neumaier

    I What is the POVM generalization of Born's rule for quantum measurements?

    I just placed my new paper Born's rule and measurement on the arXiv. It contains a self-contained discussion of the POVM generalization of Born's rule for quantum measurements. It is a much extended, polished version of my contributions to the thread How to teach beginners in quantum theory...
  3. A. Neumaier

    I How to derive Born's rule for arbitrary observables from Bohmian mechanics?

    Where can I find a reference to a derivation of Born's rule for arbitrary observables from Bohmian mechanics?
  4. E

    B Is Born's Rule Commutative in Quantum State Measurements?

    As far as I am aware, if a system is prepared in the state |r> and we measure some observable, the probability of the result of the measurement being the eigenvalue of some eigenvector |u> representing some other state is |<r|u>|2 or <r|u><u|r>. On a slightly different note, I also know that a...
  5. A. Neumaier

    A Born's rule for the QED electron violates causality

    Summary: Born's rule for the QED electron violates causality. [Since the thread where some of this material was presented was closed for further discussion, I summarize here the main content relevant for the above topic.] The free QED electron can be described in terms of a non-local...
  6. A

    I Born's rule, causality, and the Dirac equation

    [Moderator's note: Spin off from a previous thread due to topic change.] Actually, the form of the Hamiltonian does matter. Hegerfeldt admits that his results are not correct for the Dirac Hamiltonian unless one considers only positive energy solutions. And why should we do that? It is clear...
  7. Dimosthenis76

    B Is Born's rule really verified?

    Hello to everybody Is really Born's rule verified? I can not find any experiment in bibliography that verifies Born's rule.
  8. yecko

    Schrodinger equation and Born's Rule

    Homework Statement [/B] Q18. Which of the following statements about Schrodinger equation is true? A) The exact solution of the equation never exists B) It is only applicable to the hydrogen-like atoms C) We can know the energy of the atomic orbital by solving the equation D) The square of the...
  9. A. Neumaier

    I Many measurements are not covered by Born's rule

    1. Within the framework of a Hilbert space for an atom one cannot find an observable in the sense of ''self-adjoint Hermitian operator'' that would describe the measurement of the frequency of a spectral line of the atom. For the latter is given by the differences of two eigenvalues of the...
  10. G

    Possibility of violations of Born's rule in two dimensions?

    Hi, Gleason's theorem fails if the dimension of the Hilbert space is two. Does this allow for violations of Born's rule in two-dimensional systems? Or can you somehow tensor the system with the (ever-present and infinite-dimensional) Hilbert space of the rest of the universe, apply Gleason's...
  11. D

    Experimentally, how well tested is Born's rule?

    Experimentally, how well tested is Born's rule?
  12. G

    Triple-slit experiment tests the Born's rule

    http://physicsworld.com/cws/article/news/43275 ...and in another famous magazine: http://www.physorg.com/news199009831.html http://www.sciencemag.org/cgi/content/abstract/329/5990/418 http://arxiv.org/abs/0811.2068
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