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  2. Ehrenfest theorem - Wikipedia

    en.wikipedia.org/wiki/Ehrenfest_theorem

    The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force = ′ on a massive particle moving in a scalar potential (), [1]

  3. Expectation value (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Expectation_value_(quantum...

    In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...

  4. Jordan–Wigner transformation - Wikipedia

    en.wikipedia.org/wiki/Jordan–Wigner_transformation

    In what follows we will show how to map a 1D spin chain of spin-1/2 particles to fermions. Take spin-1/2 Pauli operators acting on a site of a 1D chain, +,,.Taking the anticommutator of + and , we find {+,} =, as would be expected from fermionic creation and annihilation operators.

  5. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    Download QR code; Print/export ... The expected value operator ... this means that the expected value of the sum of any finite number of random variables is the sum ...

  6. Spin (physics) - Wikipedia

    en.wikipedia.org/wiki/Spin_(physics)

    That is, the resulting spin operators for higher-spin systems in three spatial dimensions can be calculated for arbitrarily large s using this spin operator and ladder operators. For example, taking the Kronecker product of two spin- ⁠ 1 / 2 ⁠ yields a four-dimensional representation, which is separable into a 3-dimensional spin-1 ( triplet ...

  7. Angular momentum operator - Wikipedia

    en.wikipedia.org/wiki/Angular_momentum_operator

    Spin is often depicted as a particle literally spinning around an axis, but this is only a metaphor: the closest classical analog is based on wave circulation. [2] All elementary particles have a characteristic spin (scalar bosons have zero spin). For example, electrons always have "spin 1/2" while photons always have "spin 1" (details below).

  8. Complete set of commuting observables - Wikipedia

    en.wikipedia.org/wiki/Complete_set_of_commuting...

    However, if we express the Hamiltonian in the basis of the translation operator, we will find that has doubly degenerate eigenvalues. It can be shown that to make the CSCO in this case, we need another operator called the parity operator Π {\displaystyle \Pi } , such that [ H , Π ] = 0 {\displaystyle [H,\Pi ]=0} .

  9. Tensor operator - Wikipedia

    en.wikipedia.org/wiki/Tensor_operator

    A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation ...