Since the Bloch energy eigenstate functions determine the energy of space-time, we must seek to express the metric in terms of the Bloch wave functions.
The metric tensor of four-space in the k-th band is therefore associated with the Bloch energy eigenstate functions of the quantum vacuum as follows:
We expand this speed scalar potential using the energy eigenstate basis
Using the time scale [T.sub.[beta]], the time evolution in the energy eigenstate basis was found from Schrodinger-type equation to be
However, for t [greater than or equal to] 0 the particle state, which is no longer an
energy eigenstate, is given by a superposition of the
energy eigenstates [[psi].sub.k](x) (k = [square root of (E)]) of the potential [V.sub.2](x), i.e., [36]
A time interval [DELTA]t can be associated with the time function t during which is measured the energy eigenstate function E which itself has a certain width [DELTA]E, with both widths ([DELTA]) satisfying (10).
For example, we consider the impact of [DELTA]t on the observation of [[tau].sub.n], the lifetime of an atom in energy eigenstate n, and the impact of [DELTA]E on the transition energy [E.sub.mn], for a transition between states n and m during spectral line emission.
The instant-form vacuum is defined as the lowest
energy eigenstate of the instant-form Hamiltonian.
Finally, the assumption that the PV is a degenerate state implies that the Planck-particle
energy eigenstates are full.
The proton wave function could as usual be written as a superposition of
energy eigenstates