hamiltonian operator उदाहरण वाक्य

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 .)