Agreed, the quantization scheme of the Schroedinger equation as you know, is H psi = E psi where for the hydrogen atom:
H psi = (T + U) psi = ( p squared / (2m)) – e squared / (4 psi epso r)) psi
The energy levels are actually <H>, denoted E in quantum mechanics. Most students still ask: Why can’t you cross the psi? The answer is that
p squared psi = – h bar squared del squared psi
is a differential operator. Many people have immense difficulty in understanding this. We also have
<H> = – h squared integral psi* del squared psi d tau
and del squared also operates on psi. One could quantize the Sommerfeld hamiltonian as
H psi = (gamma m c squared + U) psi
As recent papers show there are hundreds of way of proceeding once the Dirac approximation is discarded.
Sent: 30/01/2016 10:38:12 GMT Standard Time
Subj: Re: Discussion of 339(1)
In quantum mechanics the expectation value of the Hamiltonian is often denoted as total energy, then E would be the kinetic total energy or so, but we know what we mean.
Am 30.01.2016 um 06:39 schrieb EMyrone:
Agreed, the hamiltonian H = E + U is always the starting point of the theory, where E = gamma m c squared is the total relativistic energy. For a free particle H = E, but any elementary particle is always interacting with vacuum, so U is always non zero.
Sent: 29/01/2016 12:48:19 GMT Standard Time
Subj: Re: 339(1): Development of the Correct Theory of Spin Orbit Structure
To recapitulate the concept of potential energy in general relativity: the “relativistic” energy
gamma m c^2
contains the kinetic and rest energy only. Any potential energy has to be introduced as an extra energy. I assume that we used this consistently in this way in all earlier papers on Dirac and similar theory.
Am 25.01.2016 um 13:31 schrieb EMyrone:
This note suggest the development of the correct theory of spin orbit fine structure before going on to a new theory of the Lamb shift. Some computer algebra is needed to evaluate Eq. (19) for the Coulomb potential.