Low-energy operators are not required to have safety sensors, as the door is allowed to come in contact with a user, given that the kinetic energy of the moving door is limited by the reduced moving speed.
32.
In RQM it is useful to take this as the zeroth Pauli matrix which couples to the energy operator ( time derivative ), just as the other three matrices couple to the momentum operator ( spatial derivatives ).
33.
When the avoided external costs are compared to the compensation that renewable energy operators were paid for electricity from renewable energy, a 2003 study finds that the reduced environmental impacts and related economic benefits far outweigh the additional costs required to compensate the producers of electricity from renewable sources.
34.
This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic wave equations, since energy and momentum combine into the 4-momentum vector above, momentum and energy operators correspond to space and time derivatives, and they need to be first order partial derivatives for Lorentz covariance.
35.
In the modern view, energy is always Hamiltonian or energy operator, the field's lowest-energy or ground state, often called the vacuum state, is not, as one might expect from that name, a state with no particles, but rather a quantum superposition of particle number eigenstates with 0, 1, 2 . . . etc . particles.
36.
In general, the on-the-mass-shell value of the self-energy operator in the momentum-energy representation is eigenstates of the underlying many-particle system, which only, if at all, momentarily behave like those specific to isolated particles; the above-mentioned lifetime is the time over which a dressed particle behaves as if it were a single particle with well-defined momentum and energy.
