0] is the

Bohr radius and v the electron pulsation (E = h v).

When the size of semiconductor nanocrystals is smaller than the

Bohr radius of the excited electron-hole pair, quantum confinement effect occurs and the band gap energy starts to increase with the decrease of particle size.

Since the uniform circular motion of an electron is in opposition to Heisenberg's Uncertainty Principle (actually [DELTA]r = 0 and [DELTA]mv = 0), my correction to special relativity allows me to consider that when the electron tends to stop, it oscillates around the origin of the x-axis with an amplitude equal to the

Bohr radius and it moves (on average) with twice the minimum speed.

Using the above given parameters of GaAs (x = 0) one can obtain the effective

Bohr radius and the effective Rydberg energy as [?

Introducing now at a separation distance s (which must correlate with the effective

Bohr radius a* of the donor and acceptor) a second Delta-doping sheet of the same kind as the first one is, a new situation for the donor-acceptor pairing is created: While close pairs within each of the doped sheets would not detect any difference, distant pairs will.

0], the

Bohr radius, gives the scale of the interaction and [gamma] is the relativistic correction factor.

Now on angular momentum, consider simply the

Bohr radius for the simplest but most general case:

However, if we consider the ratio in (11) and take one of the axes of the

Bohr radius instead of [l.

In the double surface model

Bohr radius expressed in the units of Compton wavelengths of the electron is deduced from the average path on the elliptic and hyperbolic side of the orbit:

For a single charge atom like hydrogen and lowest spin level corresponding to n = 1, we get the

Bohr radius r = [r.

Interestingly, the gravitational

Bohr radius derived from this gravitational Schrodinger equation yields prediction of new type of astronomical observation in recent years, i.

3 A new type of redshift from gravitational

Bohr radius.