heisenberg equation of motion वाक्य
उदाहरण वाक्य
मोबाइल
- It reproduces the Schr�dinger equation, the Heisenberg equations of motion, and the canonical commutation relations and shows that they are compatible with relativity.
- It is most apparent in the Heisenberg picture of quantum mechanics, where it is just the expectation value of the Heisenberg equation of motion.
- In the Heisenberg picture it is the other way round, } } is constant while evolves with time according to the Heisenberg equation of motion.
- Once the system Hamiltonian is known, one can use the Heisenberg equation of motion to generate the dynamics of a given N-particle operator.
- Moreover, this constant energy in the Hamiltonian obviously commutes with and and so cannot have any effect on the quantum dynamics described by the Heisenberg equations of motion.
- This has the same form as the corresponding classical Hamiltonian and the Heisenberg equations of motion for the oscillator and the field are formally the same as their classical counterparts.
- He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the " Heisenberg equation of motion ".
- The zero-point energy can be dropped from the Hamiltonian by redefining the zero of energy and by stating that it has no effect on the Heisenberg equations of motion:
- This is Ehrenfest's theorem, which is an obvious corollary of the Heisenberg equations of motion, but is less trivial in the Schr�dinger picture, where Ehrenfest discovered it.
- Since the states obey the Schr�dinger equation, the path integral must reproduce the Heisenberg equations of motion for the averages of and variables, but it is instructive to see this directly.
- Thus the zero-point energy can be dropped from the Hamiltonian by redefining the zero of energy, or by arguing that it is a constant and therefore has no effect on Heisenberg equations of motion.
- Note that this equation only holds when the density operator is taken to be in the Schr�dinger picture, even though this equation seems at first look to emulate the Heisenberg equation of motion in the Heisenberg picture, with a crucial sign difference:
- The Runge & ndash; Gross proof first shows that there is a one-to-one mapping between external potentials and current densities by invoking the Heisenberg equation of motion for the current density so as to relate time-derivatives of the current density to spatial derivatives of the external potential.
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