# Introduction to Quantum Mechanics

• There is a 100 year old challenge to explain Quantum Mechanics in a logical way, deriving it from the fundamental laws of Nature.

In this lecture, I aim to introduce Quantum Mechanics in a logical way:

- without violating General Relativity

- without violating Maxwell's equation

The lecture is based on our book titled Unified Field Theory and Occam's Razor. Refer to the book for further details.

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What does this have to do with nuclear structures? It is probably a good idea to firstly understand how Quantum Mechanics really works, and then consider what it implies for nuclear structures.

• This is part of a long in preparation document drawing together connections between QM and LENR, written by LENR researcher Tom Barnard. He would welcome discussion, or I am sure comparisons with Andras' presentation above.

To: those interested in a relatively easy to understand, although lengthy, LENR theory.

My last note dealt with the fusion energy loss mechanism, but perhaps I should have led with the high energy d-d bond. The behavior I propose, of the electron and two deuterons, can be described with Newtonian mechanics, much like Bohr’s original description of hydrogen atom orbits. The ‘orbits’ of this proposed intermediate do not manifest from a central force, as do ‘chemical’ bonds. The energetics of chemical bonds prevent nuclei from approaching much closer than the sum of the radii of the bonding electrons. Thus, during chemical interactions, orbits are only somewhat distorted.

If the deuterons are say, 0.1 angstrom apart, could the electron create a stationary state? At this spacing the electrostatic force can no longer be considered a ‘central force’ for the electron state. The nuclei potential presents an axial symmetric electrostatic field. A standard orbit from a central force is necessarily two dimensional, as the body is accelerated towards the center. The axial symmetry opens up the possibility of adding another dimension to the electron state. A classical description of an electron can describe an orbit circling the axial axis, while also travelling along the axis in a cork screw like motion. How/why this happens is for another note. Lower energy (higher kinetic energy) in the axial dimension gives a much shorter bond length.

Consider the analogy of a perfect ball rolling along a surface, then falling down a cylindrical hole. The ball will bounce back up and keep rolling along the same surface. Let the ball fall again, and take away some energy with another ball and the first ball can no longer escape. This is analogous to the capture of an electron by a proton to create a hydrogen atom. Now, let the ball fall in the hole again, but at the bottom it strikes an angled floor, with half the kinetic energy imparted to a spinning motion in the cylinder. Although the ball has the same total energy, it no longer has the vertical energy to escape.

Now consider a 3-dimensional harmonic oscillator for a particle. Say the force constant and energy starts out as equal in all three dimensions (spherically symmetric). The total energy is the sum from the fractional superposition of each dimension, say one third each. Let the three dimensions be in their ground state. Now let the force constants ‘magically’ increase and change to an axial symmetric form, with the axial force constant a bit higher than the two equal radial constants.

The higher axial force constant would allow a lower ground state energy level (i.e. higher kinetic energy) only if that dimension can loose energy to allow the transition. But the radial dimensions also have a higher force constant which can use the lost energy to get to a state with higher kinetic energy. Thus, the axial dimension can assume the lower energy state.

This is a crude example, but when one considers how the 1/r^2 electrostatic force changes faster and faster as the radius decreases, it isn’t far fetched and in fact works out quantitatively. The details are more complex, not because each part is hard to understand, but quantum mechanics and solid state electrons are involved.

This intermediate state bond can be described with Newtonian mechanics, unlike the bond in molecular hydrogen. Covalent bonds are not classically stable. They are only stable due to the exchange energy described by quantum mechanics. So, in that sense this intermediate bond is simpler than the covalent bond between two hydrogen atoms. Because the intermediate bond can be described with classical mechanics, there might be a quantum description for the 3 particles (electron+2d).

That’s enough for now. This is a fairly long story, with unfamiliar content, but it is a complete story, vetted quantitatively all the way through. There is no ‘magic’ beyond that of well understood basic quantum mechanics.

Regards, Tom Barnard

• This intermediate state bond can be described with Newtonian mechanics, unlike the bond in molecular hydrogen. Covalent bonds are not classically stable. They are only stable due to the exchange energy described by quantum mechanics.

This statement is plain wrong as Mills shows in his GUTCP. He calculates all molecules with classic Maxwell/Newton logic with high accuracy, that is better than classic QM but still far away from reality.

QM is a highly simplified method to approximate the energy surfaces of the coupled e/p rotation system. The "real" electron orbit has nothing in common with an oscillator, this is just the result of a highly simplified mathematical model.

QM has no clue how to model the orbital momentum of the electron and hence knows no method how the force is produced that ejects a photon.

QM does not deliver the correct image of molecular bonds, as it also neglects all second order = magnetic effects.

QM is best made to approximate electronic states in solid state compounds.

OF course QM cannot be used to explain CF/LENR as it cannot be used to model hadronic mass.

• Because the intermediate bond can be described with classical mechanics, there might be a quantum description for the 3 particles (electron+2d).

Classically, an accelerating electron radiates energy away. I wonder how he proposes that the electron would avoid acceleration in the bond. In quantum mechanics, stable bonds correspond to acceleration-free standing electron waves (wavefunctions).

As far as I know, the problem of axially symmetric molecular H2+ orbit is analytically solved in QM. This analytic solution in principle should show what inter-nuclear distances are possible.

• Alan and All,

I don’t want to get bogged down in trying to explain everything at once. It won’t work. There are too many things that are necessarily unfamiliar, but not particularly complex once the whole picture is digested. It took me a long time to become comfortable with each step. If you don’t believe QM works at the atomic level, then this discussion is not for you. The molecular modeling developed over the last 50 years are very good predictors of physical properties. This kind of modeling can only be applied to the first step of the mechanism proposed. This first step is the rate limiting step, so the most important to understand in detail. I only did a little work on this traditional molecular modeling some 10 years ago in order to demonstrate to myself that at least the first step made sense. This first step is just the formation of d2 in cracks or appropriate voids in the metal lattice. Fortunately this step is very amenable to standard molecular modeling. Olga of the now closed ‘Coolescence’ did much more extensive work on this, and reported at ICCF 18. Many thanks to Matt and Rick of Coolescence, who sponsored some of my work.

This first step simply requires the d2 bond to be less than about 0.75 Angstrom, while being associated closely with the metal lattice. If you do this modeling, you find that most circumstances will give bond lengths of 0.8 to 1.1 Angstrom. This bond length will not overlap sufficiently with my proposed intermediate to react at a reasonable rate. Although this ‘detail’ is the critical factor, it was not the interesting part of the theory to me. After all it is well understood chemical behavior. Suffice it to say there are reasonable ways to get the bond length to ~0.75 A.

I spent my time trying to piece together a logically and quantitatively consistent story. A fair number of things have to happen, and quantifying each one was somewhat beyond me at first, but I persevered, fully aware of the intellectual danger of misinterpretation that comes with leaving one’s expertise. My education is in chemistry and chemical engineering. Thus, I always tried to come at the problem from several different angles and see if the results were quantitatively consistent. The Newtonian model of an electron and 2 deuterons is an example.

I had first done the QM model of the ‘one dimensional’ state, before the Newtonian, and easily (and tediously) found the stable range of quantum bond lengths. If I had not done that, I doubt if I could have gotten the Newtonian model to work, as even the Newtonian bond isn’t stable above 0.12 A, or very small bond lengths. It took over a decade to figure out how this state could arise. As the readers can attest, it doesn’t seem to make much sense. When you see the whole picture, it makes perfect sense. I know, it doesn’t make it correct, but at least it is logically and quantitatively consistent.

I believe I’m maybe 90 to 95% there, but it needs new eyes on. I will continue to try and spark the interest of someone that could refine and publish the concept, if deemed reasonably valid. It would make for a great undergraduate level project in QM, even if found wanting.

Regards, Tom Barnard

• Classically, an accelerating electron radiates energy away. I wonder how he proposes that the electron would avoid acceleration in the bond. In quantum mechanics, stable bonds correspond to acceleration-free standing electron waves (wavefunctions).

As far as I know, the problem of axially symmetric molecular H2+ orbit is analytically solved in QM. This analytic solution in principle should show what inter-nuclear distances are possible.

Andras! You wrote - "Classically, an accelerating electron radiates energy away." Especially for you and for people like you, I investigated Maxwell's errors ... I found 6 errors in Maxwell's section "Electrostatics" ... Especially for you in another thread I explained why there are no charges on the electron and proton - "electrostatic charges". - Say a word about "poor" Charles Coulomb... How the name of the great French scientist was denigrated...

It is the absence of charges on the proton and electron that explains the absence of an "electric field" in nature ... Therefore, the absence of an "electric field" in nature means the absence of "electric forces" in nature - this in turn means that there are no forces in nature that accelerate the electron ... You have been deceived ... We have been deceived ... Realize this and reconsider your attitude to quantum mechanics - there is nothing in nature that obeys mathematics, which is presented in quantum mechanics ... Quantum mechanics is no longer a science! I wish you success in understanding the truth.

• Classically, an accelerating electron radiates energy away. I wonder how he proposes that the electron would avoid acceleration in the bond. In quantum mechanics, stable bonds correspond to acceleration-free standing electron waves (wavefunctions).

The non radiation condition, detected by Hauss, contradicts this assumption. There are stable orbits where there are no time like contributions in the wave function. (Also see Mills).

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