This note begins a new numerical development of quantum mechanics and relativistic quantum mechanics starting from the classical lagrangian, then quantizing the results. This first note is a simple idealized atom modelled by an electron orbiting a proton in a plane. It could also be applied to quantize the usual conic section orbit of a mass m orbiting a mass M in a plane. After quantization, two simultaneous equations (17) and (18) are found. These can be solved for psi(r) and psi(phi). In the Born Oppenheimer approximation the complete wavefunction is psi = psi(phi)psi(r). It may be argued that these can be found analytically with well known methods, but the advantage of this numerical method is that it can be extended to three dimensions and to a new development of relativisic quantum mechanics. It gives a new method for computational quantum chemistry in general, given the supercomputer power. The Dirac equation, for example, can be solved in a new way. The Maxima code is very powerful and contemporary desktops are also very powerful. We begin with this baseline problem so that the numerical results can be checked against known analytical results, notably the non relativistic orbitals of the lodestone of quantum mechanics, the H atom. Numerical mthods such as these can also be applied ot the ECE wave equation inferred in 2003.
Archive for February, 2017
Kocaeli is a new university, is ranked 1841 in the world by webometrics and has over 52,000 students, founded in 1977. It is mainly technical but also has a fine arts faculty. UFT88 is a famous paper in scientific circles, and to the very large folloing of ECE theory, refutes the Einsteinian general relativity through consideration of torsion. It has been developed into UFT313, and should be read with UFT99 and UFT109, together with UFT354. It is the paper that epitomizes van der Merwe’s post Einsteinian paradigm shift, now widely accepted as mainstream physics. The Einstein theory has been replaced by ECE2, of which there are currently fifty six papers and books, all read around the world every day.
OK many thanks, this Runge Kutta method is a very powerful Maxima algorithm, and can be applied now to give a large amount of new results for many problems of ECE2 theory. I will write out the equations of most interest. For spherical orbits it will be very interesting to plot the true orbit r = alpha / (1 + epsilon cos beta) obtained from the Hooke Newton inverse square law using spherical polar coordinates. No modelling assumption is made other than the usual inverse square law.
Sent: 27/02/2017 17:38:36 GMT Standard Time
Subj: Re: 371(4): Scheme of Computation for the 3D Orbit
Basically thre are two methods of solving the central motion in a spherical polar coordinate system: Either the full set of Lagrange equations without constants of motion or by predefining L and L_Z and solving (19-22). I will try the latter. These equations are only of first order for beta, theta, phi so they reduce the number of Hamilton equations used for the Runge-Kutta solution method.
Am 26.02.2017 um 14:19 schrieb EMyrone:
This note gives the scheme of computation that gives all information about a spherical orbit governed by an inverse square force law of attraction. Maxima can now be used to compute any type of information needed, notably the orbits r(beta), r(theta) and r(phi). Some of the analytical results from UFT270 to UFT276 on three dimensional orbits are reviewed. The planar orbit is recovered in the limit theta goes to pi / 2, theta dot goes to zero. The planar orbit is given by Eq. (33), and does not precess for an inverse square law as is well known. In three dimensions however it precesses in various ways. There is a typo in Eq. (31), which should read theta goes to pi / 2. We are now ready to use Maxima for the lagrangian in ECE2 relativity, both for planar and three dimensional orbits.
As usual there was intense international interest from the best universities, institutes and similar in the world, including visits from seventeen of the top twenty universities in the world as ranked by Webometrics, Times, QS and Shanghai world university rankings (* denotes repeat or multiple visits): Caltech, Harvard*, Princeton, Penn State*, Stanford, Texas A and M*, UC San Diego, EPF Lausanne*, ETH Zurich*, Cambridge, Oxford*, Imperial, Edinburgh, Cornell, Chicago, UCLA and Wisconsin Madison. The attached represents only about 2% of the vast readership of www.aias.us, sustained since 2002 and archived in real time on www.archive.org and www.webarchive.org.uk using Wayback Machine software. Combined sites www.aias.us and www.upitec.org are displayed as sites of national importance in science and culture in the reading rooms at the copyright libraries in Britain and Ireland: British Library London, Bodleian Library Oxford, University of Cambridge Library, National Library of Scotland Edinburgh, National Library of Wales Aberystwyth, Library of Trinity College Dublin in Ireland. Many congratulations to all staffs on another outstanding performance. The final returns for February 2017 will be in as usual in two days’ time. It is clear that ECE and ECE2 are mainstream physics, and that our distance teaching and research publication methods have been spectacularly successful in up to 182 countries.
The wind speed in the Betws area now is an average of 10 mph, effective wind speed of 1 mph, because it takes 9 mph to start the turbines, so they are producing effectively nothing but grid instability, “A drunk man looks at the thistle” in the words of the great Scots and English language poet Hugh MacDiarmaid, one of the founders of the Scottish Nationalist Party and Civil List Pensioner 1950. Solar is again zero, an asbolutely brilliant achievement. Hydro is a dismal 2.84%, nuclear is flat out and gas is close to flat out to try to meet the heavy demand. Coal is also fired up and increasing. Wind has again failed completely this morning. So whoever formulated this crazy policy is an expert in drunken Brownian motion, random chaos (see my early Omnia Opera works on www.aias.us).
The equivalent of 40,940 printed pages was downloaded (149.261 megabytes) from 1,676 memory files downloaded and 387 distinct visits each averaging 4.5 memory pages and 5 minutes, top referrals 2,213,162, printed pages to hits ratio of 24.43, main spiders Google, MSN and Yahoo. Collected ECE2 1191, Top ten 1120, Collected Evans / Morris 858(est), Collected scientometrics 540, F3(Sp) 371, Barddoniaeth 289, Principles of ECE 137, Eckardt / Lindstrom 131, Autrobiography volumes one and two 127, Collected Proofs 93, Engineering Model 83, Evans Equations 71, UFT88 70, PECE 50, CEFE 45, ECE2 43, UFT311 43, Self charging inverter 35, Llais 25, UFT321 25, PLENR 11(est), UFT313 21, UFT314 19, UFT315 17, UFT316 17, UFT317 28, UFT318 17, UFT319 20, UFT320 18, UFT322 22, UFT323 16, UFT324 18, UFT325 26, UFT326 18, UFT327 16, UFT328 27, UFT329 21, UFT330 15, UFT331 20, UFT332 14, UFT333 20, UFT334 15, UFT335 19, UFT336 14, UFT337 16, UFT338 13, UFT339 13, UFT340 13, UFT341 23, UFT342 11, UFT343 17, UFT344 22, UFT345 15, UFT346 15, UFT347 21, UFT348 15, UFT349 19, UFT351 20, UFT352 28, UFT353 26, UFT354 31, UFT355 17, UFT356 26, UFT357 27, UFT358 21, UFT359 20, UFT360 19, UFT361 12, UFT362 23, UFT363 22, UFT364 24, UFT365 16, UFT366 45, UFT367 42, UFT368 44, UFT369 46, UFT370 30 to date in February 2017. State University of New York Buffalo UFT213; University of Notre Dame UFT142; Ecole Superieure of Industrial Physics and Chemistry of the City of Paris (ESPCI) UFT330; Isfahan University of Technology Iran Essay 24; Bahria University Karachi Pakistan UFT41. Intense interest all sectors, updated usage file attached for February 2017.
The referring domains data every early morning refers to the single top domain of many thousands. Today it is 2,212,935 since December 2006. Total referrals are probably over three million. The top referring domain total increases rapidly every day. Early personal attacks on myself have been overwhelmingly rejected. They cannot be called rational criticisms, more like trolling. The only site of this type that gets any professional attention is one by Bruhn, with 65 referrals in a decade. He disappeared in 2008 after harassing, stalking and trolling for about five years. Cartan geometry is the same as it was in 2003, and the attacks on Cartan geometry by these people have of course failed. They attacked Cartan geometry because I used it in an imaginative way. Nothing as stupid as this has ever happened in science. ECE theory is based directly on Cartan gemetry, which is why it has been overwhelmingly accepted internationally by all the best universities, institutes and similar in the world. Wikipedia on ECE is a failed troll site set up by a few people like Bruhn whose only aim in life was destruction – a low point in the history of science. A criminal troll site has been operating for about three years, and has generated a glorious total of 32 referrals. In my opinion these trolls should be rooted out and arrested by the police. Several are local and I can identify them by style of writing. The policy of AIAS / UPITEC for some years is to ignore them completely and to report them to the police as part of the duty of any member of the general public to report hate crime. It is up to the police to act against them.
I will prepare a few lagrangians of interest for numerical solution. Some very interesting results will probably emerge.
I will write to or go to see the Secretary, Deacon and Trustee, Mr Alistair Davies, 57 Ty’n y Coed, Pontardawe, SA8 3DJ, tel. 01792 864208, in order to donate to the Elim Baptist Chapel Trust and discuss the restoration of the organ. Most of it is in good condition. My overall aim is one of conservation, traditional in the Havard Family. It may be possible to have the chapel listed by CADW. Ysgrifenaf i Alistair Davies i siarad ag ef am rhodd i’r capel, i gyweirio’r organ. Mae rhan fwyaf o’r organ mewn sefyllfa da. Mae angen edrych ar ol y Capel a chapeli eraill yn yr ardal. There is a need to look after this chapel and other chapels in Mawr. Each chapel is independent of any Secular Council.
These should come online as rapidly as possible. The ECE theory needed to understand ES power stations is available (UFT311), and the patented Osamu Ide circuit has been replicated by Horst Eckardt et al in UFT364. The Assembly should push ahead with raising the funds to develop all kinds of power devices based on ES, which has no moving parts and works on all scales, from microchips to major power stations. The ECE theory has been an international team effort, and was started here in Mawr. If a coal /oil cabal exists, it will shortly become extinct. The circuit can be demonstrated to the Assembly at any time.