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2020년 12월 26일 (토) 05:26 판

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  1. Hamiltonian operator, a term used in a quantum theory for the linear operator on a complex ► Hilbert space associated with the generator of the dynamics of a given quantum system.[1]
  2. Operating on the wavefunction with the Hamiltonian produces the Schrodinger equation.[2]
  3. The full role of the Hamiltonian is shown in the time dependent Shrodinger equation where both its spatial and time operations manifest themselves.[2]
  4. In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.[3]
  5. The Hamiltonian of a system is the sum of the kinetic energies of all the particles, plus the potential energy of the particles associated with the system.[3]
  6. Although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes.[3]
  7. The Hamiltonian generates the time evolution of quantum states.[3]
  8. σ z /2, represents the internal Hamiltonian of the spin (i.e., the energy observable, here given in units for which the reduced Planck constant, ℏ = h/(2π) = 1).[4]
  9. The dominant term of the internal Hamiltonian represents the action of a strong magnetic field applied to the sample.[4]
  10. We will use the Hamiltonian operatorwhich, for our purposes, is the sum of the kinetic and potential energies.[5]
  11. This RRHO Hamiltonian combines the kinetic energy elements of both previous models as well as an associated potential energy (as that in the harmonic oscillator scenario).[6]
  12. This version of the Hamiltonian looks more complicated than Equation \ref{7-7}, but it has the advantage of using variables that are separable (see Separation of Variables).[7]
  13. In the field of quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.[8]
  14. In my post on the post on the Hamiltonian, I explained that those C i and D i coefficients are usually a function of time, and how they can be determined.[9]
  15. We introduced operators – but not very rigorously – when explaining the Hamiltonian.[9]
  16. Well… It turns out his Hamiltonian operators is useful to calculate lots of stuff.[9]
  17. The deeper problem with this supposition is that it assumes a conceptual identity between the notions of Hamiltonian and energy, and this is an identity that is not correct.[10]
  18. The Hamiltonian, on the other hand, is a mathematically modified version of the Lagrangian, through what is called the Legendre transform.[10]
  19. What this equation is "really" saying is that in order for such a time series to represent a valid physical evolution, the Hamiltonian must also be able to translate it through time.[10]
  20. Typically being a non-unitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli string terms.[11]
  21. Here, we show how to approximate the Hamiltonian operator as a sum propagators using a differential representation.[11]
  22. Its Hamiltonian is often called the Hamiltonian.[12]
  23. The eigenvalues of the Hamiltonian operator for a closed quantum system are exactly the energy eigenvalues of that system.[12]
  24. Thus the Hamiltonian is interpreted as being an “energy” operator.[12]
  25. In the example below, the Hamiltonian Operator node inputs the Hamiltonian of a harmonic oscillator and applies it to a Gaussian function to give a new function.[13]
  26. The Hamiltonian operator, H, is patterned after those discussed previously for the one electron "box" and atom.[14]
  27. The above definitions show that the Hamiltonian operator depends in a simple and obvious way on a molecule's composition.[14]
  28. First, note that the electronic Hamiltonian contains three sums.[14]
  29. We focus on partial Hamiltonian systems for the characterization of their operators and related first integrals.[15]
  30. Firstly, it is shown that if an operator is a partial Hamiltonian operator which yields a first integral, then so does its evolutionary representative.[15]
  31. Secondly, extra operator conditions are provided for a partial Hamiltonian operator in evolutionary form to yield a first integral.[15]
  32. Thirdly, characterization of partial Hamiltonian operators and related first integral conditions are provided for the partial Hamiltonian system.[15]
  33. The hamiltonian class wraps most of the functionalty of the QuSpin package.[16]
  34. basis basis : basis used to build the hamiltonian object.[16]
  35. Returns copy of a hamiltonian object at time time as a scipy.sparse.linalg.[16]
  36. copy () Returns a copy of hamiltonian object.[16]

소스

  1. ↑ Hamiltonian Operator
  2. ↑ 2.0 2.1 The Hamiltonian in Quantum Mechanics
  3. ↑ 3.0 3.1 3.2 3.3 Hamiltonian (quantum mechanics)
  4. ↑ 4.0 4.1 Hamiltonian Operator - an overview
  5. ↑ The Hamiltonian Operator
  6. ↑ Quantum Mechanical H Atom
  7. ↑ 7.2: The Hamiltonian Operator for Rotational Motion
  8. ↑ Hamiltonian Operator
  9. ↑ 9.0 9.1 9.2 Hamiltonian operator – Reading Feynman
  10. ↑ 10.0 10.1 10.2 Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?
  11. ↑ 11.0 11.1 Hamiltonian operator approximation for energy measurement and ground state preparation
  12. ↑ 12.0 12.1 12.2 Hamiltonian in nLab
  13. ↑ Hamiltonian Operator
  14. ↑ 14.0 14.1 14.2 box
  15. ↑ 15.0 15.1 15.2 15.3 Characterization of partial Hamiltonian operators and related first integrals
  16. ↑ 16.0 16.1 16.2 16.3 quspin.operators.hamiltonian — QuSpin 0.3.4 documentation

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