Quantum Mechanics

As with any scientific model it can not be stated to be absolutely without error.

However it is confirmed to extremely high numerical precision in all tests that have been performed to the present time. It would take experiments detecting very very tiny but both consistent and statistically significant discrepancies to change it.

He does not form a chemical compound. The He2 molecule is not knon. The He2+ cation has a very transient existence and has a reportedly very short bond length of approximately 0.75 Angstrom.

When certain combinations of protons and neutrons form an atomic nucleus, there is the possibility that the nucleus may be unstable. There may be too few or too many protons for the number of neutrons present, or there may be too few or too many neutrons for the number of protons present. In any case, if the nucleus is unstable, that nucleus is said to be radioactive. There is another case in which a nucleus can be unstable, and that is that it is simply too large to be able to stay together. Recall that nuclear binding energy holds atomic nuclei together, and it overcomes the electromagnetic repulsion of the positively charged protons to do this. But when atoms become "really big" as we see them at the top end of the periodic table, they are uniformly unstable. They are all radioactive and will eventually undergo nuclear decay of some kind. In a radioactive substance, the instability of the nuclei of the atoms will eventually "win out" over the binding energy holding the nuclei together, and the nucleus will "fall apart" or even "split" in some cases. Is there a "magic number" associated with the disproportionality that will tell us if a given atom is unstable? No, there isn't. We have to look at things on a case by case basis. Recall that atoms of the same element that have differing numbers of neutrons in them are isotopes of that element. And for a given element, some unstable isotopes exist. They may appear in nature, or we may see them in the physics lab. In addition to the existence natural or synthesized radioactive isotopes of the elements, some elements have no stable isotopes whatsoever. That means all isotopes of those elements are radioisotopes, and are radioactive. You probably recall the element technetium, which has no stable isotopes. That's an example, and we see more examples at the "top end" of the periodic table where the nuclei of the elements are huge. The binding energy or nuclear glue holding the nuclei together is losing ground to the repulsive forces of all the positively charged protons. Eventually we'll reach a point where a massive nucleus won't stay together, no matter what.

Quantum entanglement "does not exist" !!! If / when Hydrogen reaches singularity, the strong & weak nuclear forces are no longer required ! The only forces to remain are the Gravitational & the Electromagnetic !!!

Individual atoms are about one angstrom in size.

Sound waves -- the vibrations of matter that we can hear -- must have wavelengths of at least (about) .005 meters, or 5,000,000,000 angstroms.

Now a COLLECTION of atoms -- in any state of matter -- can indeed cause and propogate sound waves, and individual ones have a certain probability of reacting to those vibrations within that collections. But this probability is lower than that of a reaction due to heat or light in the medium carrying the sound.

When an individual atom changes it energy state, it emits a photon, which is FAR different from releasing a sound.

I am checking the Wikipedia article on "quantum number", and don't find a quantum number "i" for the electron. If you mean "l", it seems that "l" can be between 0 and n-1. So, for n = 3, l can be between 0 and 2. If this is what you mean, I don't see any reason that would forbid this particular combination.

You are referring to the Schrodinger Equation. This is because it comes from the classical view that the total energy is equal to the hamiltonian of a system:
Kinetic Energy + Potential Energy = Total energy.
Classically the kinetic energy is (1/2)mv2 = p2/(2m) ; where m is mass, v is velocity, p is momentum (p=mv).
Now the momentum operator in QM is p=iħ∇ ;where ∇ is the gradient operator.

This therefore yields the QM hamiltonian [-ħ2∇2/(2m) + V(x,y,z)]Ψ = EΨ

Now a more fun question to ask would be "Why is the Hamiltonian a function of the second-order partial differential with respect to position but the time dependent is only a function of a first-order differential with respect to time?"

meaning
HΨ = -iħ(dΨ/dt) or
[-ħ2∇2/(2m) + V(x,y,z)]Ψ = -iħ(dΨ/dt)

hint: Think Maxwell's Equations!

The Schrödinger wave equation cannot be derived (at least not by any known means). Erwin Schrödinger literally guessed the equation (though his guess had reason behind it), and justification for its use can be attributed to the simple fact that it works.

Thought it was guess when Schrödinger formulated his wave equation he drew from a classical foundation. Total energy is equal to the kinetic energy plus the potential energy. Classically kinetic energy is expressed as p2/(2m), where p is momentum and m is the mass. The potential can be whatever you want it to be so we will just call it V, then finally lets call the total energy E. We put this all together to get p2/(2m)+V=E but in terms of operators p=[i*h/(2*pi)]*(d2/dqi2), where i is the square root of negative one, h is Planck's constant, pi is 3.141529, and (d2/dqi2) is the second order differential with respect to space in generalized coordinates. So putting p back in our equation for energy we get [- h2/(4*pi*m)]*(d2/dqi2)+V=E. Now comes the sort of complex part. In general the total energy of a system is defined by the Hamiltonian, lets call is H. Now, E is the eigenvalue of the Hamiltonian operator. Meaning that when H operates on some state it is measuring the total energy of that state. In quantum mechanics H=[i*h/(2*pi)]*(d/dt), where (d\dt) is the first order differential with respect to time. Now putting this all together we get [i*h/(2*pi)]*(d/dt)=[- h2/(4*pi*m)]*(d2/dqi2)+V. That, to me, is Schrodinger's "picture" of the wave equation.

-

Sorry it is a bit lengthy but I wanted to be thorough.

Baryons are particles composed of three, "color-neutralizing" quarks. Protons and neutrons are the most well-known examples.

Mesons are particles composed of a quark/antiquark pair. The pion is the best-known example.

The Higgs Boson, if it exists, should be a massive point particle, so there should be nothing "in" it.

Did you mean normalization or renormalization?

Normalization involves determination of constants such that the value and first determinant of each segment of a wave function match at the intersections of the segments.

Renormalization is a process to remove infinities from a wave function.

The math in quantum mechanics uses complex numbers; these can be considered to have a real part and an imaginary part ("Cartesian coordinates"); however, they can also be described, alternatively, by a magnitude and an angle. This latter form ("polar coordinates") is especially appropriate for doing multiplications.

No, because is n=1, the electron is in the first energy level, therefore cannot have a l=2, because l= n-1. Or more simply put l=2 is a d-orbital, and there are no d-orbitals in the first energy level. ml=0 is correct because ml= +-l through 0.

not only is it possible but no experiment has ever been done that contradicts it in any way. it has been shown correct in its predictions to more digits than any other theory.

There is a "belief" among a group of investigators, usually metaphysical types, that all things vibrate. This is absolutely true on an atomic or molecular scale, but not on a macroscopic one. People do not "vibrate" at a given frequency. There are some individuals who claim to detect the "vibration" of a person, but just what is being detected is not clear.

1200 newtons

The fullform of APPLE stands for: Ariane Passenger Payload Experiment.

h-bar (the letter "h" with a horizontal line) is equal to Planck's constant, divided by (2 x pi). Wikipedia says the following about this: "In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of rotations per second or Hertz) it is often useful to absorb a factor of 2Ï€ into the Planck constant." In other words, when there is a rotation, or a distance around something (as in an electron's path around the atom), the factor 2 x pi appears quite naturally; so the h-bar is used as a convenient shortcut.

Mechanical energy depend on motion and height. For example- a flying bird.

Plasma, found all over the Universe, common examples: stars, neon signs, and some cutting and welding equipment.

Codes for the in-game shop "Valencia" in AdventureQuest Worlds are special codes that players can redeem for exclusive items, gear, or other rewards. These codes are usually given out during special events, promotions, or by the game developers as a way of giving back to the player community. Keep an eye on the game's official social media channels, websites, or forums for announcements regarding these codes. You can also try doing a quick search online to see if any active codes are available.

Only one, all neutrons are "identical" and indistinguishable.

Quite a lot. In developed countries, hardly a home DOESN'T have laser equipment. (Reminder: both CDs and DVDs use laser.) Lasers are also used for certain surgeries, for precision measurements, and for other purposes. You may want to read the Wikipedia article on "Laser" for more details.

Einstein believed that a quantum state for sub-atomic particles existed prior to it being measured; Bohr believed that the quantum state was fundamentally unknown prior to a measurement. This idea is called "realism." As Einstein stated, "I like to think the moon is there even if I am not looking at it."

For many decades this debate was more philosophical than scientific, as there wa no experiment to determine which model was more correct.

In the last couple of decades, experiments have unambiguously disproved the idea of "local realism." In our Universe, one of two things MUST be true:

1) Prior to measurement, the quantum state of a photon does not exist.

2) Photons can communicate their quantum state to another photo faster than the speed of light.

Scientists are still debating which is true, and under what specific circumstances. But experiments clearly show they can not BOTH be false.