hamiltonian operator वाक्य
उदाहरण वाक्य
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- This yields to a Hamiltonian whose eigenvalues are the square of the imaginary part of the Riemann zeros, and also the functional determinant of this Hamiltonian operator is just the Riemann Xi function.
- In RS theory one considers an unperturbed Hamiltonian operator \ hat { H } _ { 0 }, to which a small ( often external ) perturbation \ hat { V } is added:
- To apply the Schr�dinger equation, the Hamiltonian operator is set up for the system, accounting for the kinetic and potential energy of the particles constituting the system, then inserted into the Schr�dinger equation.
- This means that the state at a slightly later time differs from the state at the current time by the result of acting with the Hamiltonian operator ( multiplied by the negative imaginary unit, ).
- As an application, we consider the Schr�dinger equation, or equivalently, the Hamiltonian operator " H " models the total energy observable of a quantum mechanical system "'S " '.
- "Fractional quantum oscillator " introduced by Nick Laskin ( see, Ref . [ 2 ] ) is the fractional quantum mechanical model with the Hamiltonian operator H _ { \ alpha, \ beta } defined as
- The tensor product factorization is only possible if the orbital and spin angular momenta of the particle are separable in the Hamiltonian operator underlying the system's dynamics ( in other words, the Hamiltonian can be split into the sum of orbital and spin terms ).
- The Lagrangian approach with field interpretation of is the subject of QFT rather than RQM : Feynman's path integral formulation uses invariant Lagrangians rather than Hamiltonian operators, since the latter can become extremely complicated, see ( for example ) S . Weinberg ( 1995 ).
- Solving the latter in any particular case requires specifying the Hamiltonian operator, which includes a generic part related to kinetic energy and specific part related to how the particle ( s ) potential energy can be expected to change as a function of position and / or time.
- A very important aspect of the Hamiltonian operator is that it only acts at vertices ( a consequence of this is that Thiemann's Hamiltonian operator, like Ashtekar's operator, annihilates non-intersecting loops except now it is not just formal and has rigorous mathematical meaning ).
- A very important aspect of the Hamiltonian operator is that it only acts at vertices ( a consequence of this is that Thiemann's Hamiltonian operator, like Ashtekar's operator, annihilates non-intersecting loops except now it is not just formal and has rigorous mathematical meaning ).
- Where " E " = total energy, " H " = hamiltonian, " T " = kinetic energy and " V " = potential energy of the particle, substituting the energy and Hamiltonian operators and multiplying by the wavefunction obtains the Schr�dinger equation
- In which \ psi is the wavefunction of the system, H is the Hamiltonian operator, and T and V are the operators for the kinetic energy and potential energy, respectively . ( Common forms of these operators appear in the square brackets . ) The quantity " t " is the time.
- There are however severe difficulties with this particular approach, for example the Hamiltonian operator is not self-adjoint, in fact it is not even a normal operator ( i . e . the operator does not commute with its adjoint ) and so the spectral theorem cannot be used to define the exponential in general.
- Where \ hat H is the Hamiltonian operator, T is elapsed time, E is the energy change due to the disturbance, W =-E T is the change in action due to the disturbance, \ varphi is the field of the virtual particle, the integral is over all paths, and the classical action is given by
- Sen's initiation and completion by Ashtekar, finally, for the first time, in a setting where the Wheeler DeWitt equation could be written in terms of a well-defined Hamiltonian operator on a well-defined Hilbert space, and led to construction of the first known exact solution, the so-called Chern Simons form or Kodama state.
- The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely related . ( Specifically, only two-point'Green's functions'in the case of a non-interacting system are Green's functions in the mathematical sense; the linear operator that they invert is the Hamiltonian operator, which in the non-interacting case is quadratic in the fields .)
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