The Scalar R

Feed: Dr. Myron Evans
Posted on: Wednesday, April 20, 2011 11:21 AM
Author: metric345
Subject: The Scalar R

Many thanks in turn! I am about ready to write up UFT 179 on the new discovery that the energy equation of general relativity has the same format as the Einstein energy equation of special relativity, provided the measured mass m0 is replaced by the covariant mass. The latter can be found from metrical methods. So the fermion and Schroedinger equations have the same format in general relativity, the mass m0 being replaced by the covariant mass m. This method predicts a large number of new spectral effects. The covariant mass of UFT 158 ff. can also be obtained from metrical methods. The covariant mass m is related to R by:

R = (mc / h bar) squared

so R can also be found from metrical methods.

View article…

Advertisements

Implementation of the Code Package WIEN for Force Eigenvalues

Feed: Dr. Myron Evans
Posted on: Wednesday, April 06, 2011 7:03 AM
Author: metric345
Subject: Implementation of the Code Package WIEN for Force Eigenvalues

It could be that more up to date versions of code address this problem more and more accurately as computers become faster and more powerful. Probably there are iterative procedures for finding the right spectrum after first omitting kappa. The 2 x 2 matrix method looks very interesting. Novak’s starting equations (15) and (16) certainly give the complete H spectrum as shown in Merzbacher and numerous other textbooks. The method given by Atkins also gives the complete H spectrum. The Novak method omits the last term on the LHS of his eq. (17), but retains the l (l + 1) term. However, in his eq. (19) he uses kappa (kappa + 1) = l(l + 1), and this is not self consistent because l(l +1) is first assumed to be zero, then in eq. (21), non-zero. It should be possible to solve eq. (17) of Novak with computer algebra to get g with no approximations, and then get the forces using

(H hat – epsilon) del g = F g

View article…

Corrigenda Note 178(5)

Feed: Dr. Myron Evans
Posted on: Wednesday, April 06, 2011 7:16 AM
Author: metric345
Subject: Corrigenda Note 178(5)

Thanks to Dr Horst Eckardt for two corrigenda:

1) In Eq. (19), replace minus by plus before (epsilon – V) / (2 m c squared).
2) In Eq. (30) the first term is plus and second term minus.

These slips do not affect the final result (41). The mass term is given by some authors and not by others (e.g. Ryder does not give it, and he omits the spin orbit and Darwin terms). It comes from the non-relativistic approximation of kinetic energy given in eq. (22), i.e. epsilon about p squared / (2m). This approximate epsilon is then put back in the third RHS term of eq. (21) to give:

sigma dot p p squared sigma dot p phi / (8 m cubed c squared) = p fourth / (8 m cubed c squared)

with p = – i h bar del.

View article…

The Hamiltonian and Quantum Mechanics

Feed: Dr. Myron Evans
Posted on: Monday, March 28, 2011 11:32 PM
Author: metric345
Subject: The Hamiltonian and Quantum Mechanics

Quantum mechanics derives directly from the hamiltonian of Rowan Hamilton:

H = T + V = E

This gives

H hat psi = E psi

which is Schroedinger’s equation with the axiom

p hat psi = – i h bar partial psi / partial x

where psi is a function operated upon by p hat. So

T hat psi = – h bar squared / (2m) partial sup 2 psi / partial t squared

so

H hat psi = (T hat + V) psi = E psi

where T hat is a second partial differential and V and E simply multiply psi.

I am not sure how many students really understand this. My Ph. D. supervisor admitted that he did not, after many years of lecturing on it. So how could his students have really understood it? The new quantum Hamilton equations and new force equation go much deeper than Schroedinger and Heisenberg ever did. So there is plenty of scope for grant applications just on UFT 176 and 177 alone, never mind all the other work going back to 1973. That is if you are minded in that way. There is nothing wrong with making grant applications, but I am basically a problem solver and it is essential to work almost full time on that in order to make real progress. So grant money to AIAS (as it fully deserves) must come in via organization of fund applications by other members of AIAS. Grant money in science usually comes in for fashionable trends – just as in any walk of life.

View article…

177(2): Zero’th Force Eigenvalue of the Harmonic Oscillator

Feed: Dr. Myron Evans
Posted on: Wednesday, March 23, 2011 4:27 AM
Author: metric345
Subject: 177(2): Zero’th Force Eigenvalue of the Harmonic Oscillator

The new force equation of quantum mechanics is eq, (1), and the harmonic oscillator gives a zero point force eigenvalue:

F sub 0 = – k x

This is the classical result of Hooke’s law, meaning that the well know zero point energy:

E sub 0 = h bar omega / 2

is accompanied by a hitherto unknown zero point force which happens to have the classical value of Hooke’s law. Eq. (1) is a new fundamental equation of quantum mechanics and can be applied to any problem. I suggest that Horst and I apply it in UFT 177 to the first few wavefunctions of the harmonic oscillator and the first few radial functions of the H atom to make the first exploration of force eigenvalues. Eq. (1) has an unlimited number of applications in quantum mechanics and derivative subject areas of QM such as quantum optics and quantum field theory. My hand calculations of this note can also be checked as usual by computer algebra. The Casimir force originates in F sub 0.

a177thpapernotes2.pdf

View article…

Final Version of UFT 176

Feed: Dr. Myron Evans
Posted on: Tuesday, March 22, 2011 6:44 AM
Author: metric345
Subject: Final Version of UFT 176

This is the final version of UFT incorporating a new result in eq. (13):

F psi = E d psi / dx

a176thpaper.pdf

View article…

Pure Quantum Version of Eq. (21) of UFT 176

Feed: Dr. Myron Evans
Posted on: Friday, March 18, 2011 1:05 PM
Author: metric345
Subject: Pure Quantum Version of Eq. (21) of UFT 176

This is as follows:

partial (H hat psi) / partial x = i h bar d (partial psi / partial x) / dt

with
H hat psi = H psi = E psi

E = H = T + V

View article…

Advertisements