The continuous and discrete spectra of physical systems can be modeled in functional analysis as different parts in the Hamiltonian operator.
12.
One particularly important representation, is that in which the transformed Hamiltonian operator \ hat { H }'_ 0 is diagonalized.
13.
By contrast, in quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with experimental observations.
14.
Thus the symmetry group of the two particle Hamiltonian operator is the superset of the symmetry groups of the Hamiltonian operators of individual particles.
15.
Thus the symmetry group of the two particle Hamiltonian operator is the superset of the symmetry groups of the Hamiltonian operators of individual particles.
16.
In the Schr�dinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy.
17.
Thus, what we think about as time evolution of any physical system is just a gauge transformation, similar to that of kernel of the Hamiltonian operator.
18.
To demonstrate this, they picking up on Fermi's trick which allows to identify an arbitrary wavefunction as a stationary state for some Hamiltonian operator.
19.
Where \ hat { H } is the Hamiltonian operator, and is the Hamiltonian represented in coordinate space ( as is the case in the derivation above ).
20.
Where is the wavefunction of the system, is the quantum Hamiltonian operator, rather than a function as in classical mechanics, and is the Planck constant divided by 2.
