Quantum Mechanics

It has to do with the energy level accessible to the electron in a particular type of bond or orbital. The difference between the two energy levels determines the energy of the quantum step and consequently the frequency of the light absorbed or emitted.

The 4th dimension is a reality, not man made. The 4th dimension is not like the other three dimensions. The mathematics and physics of the dimensions are not understood by most people.

The first three dimensions are vector dimensions and describe the three dimensions of space say , x,y and z. These dimensions were the first dimensions discovered and they are thought to be real dimensions. Real dimensions are like real numbers, their square is a positive number. The truth is the first three dimensions are vectors and are geometrical dimensions. Vectors have relationships like parallel and perpendicular. so v1 and v2 can be parallel to each other or perpendicular to each other. The relationahip betweenvectors involves the angle between them so v1.v2 = v1v2cos(a) and if cos(a) is zero the angle is an odd multiple of 90 degrees, perpendicular. The cos(a) is unity if the angle is an even multiple of 90 degrees. Minus unity means the vectors are Parallel, pointing in the same directon. Plus Unity means the vectors are anti-parallel, the vectors are pointing in opposite directions.

Everyone is roughly familiar with the vector dimensions, except that scientists and mathematicians want the square of vectors to be positive not negative. This is a mathematical defect that ruins vectors.

The 4th dimension is not a vector it is a plain old real number sometimes called a scalar number. Sclars or eeal have positive squares. Scalars are not vectors. Scalars are critically important in science and mathematics. The reason is best understood when you ask the question "What happens to the vectors when you multiply two parallel two vectors v1 and v2? The answer is, the product of two parallel vectors is not a vector! This is like smashing two oranges together and the oranges disappear and turn into a banana. This is called lack of Closure in mathematics. Closure says that If A and B are vectors, then AB is a vector. You could say Human's beget Humans and fish beget fishes. This is the idea of Closure. Vectors don't have Closure. In Physics they would say that vectors transmuted into a real number. Physicists would create a table of "particles Realtionships". Two reals produce a real; a real and a vector produce a vector; two vectors produce a negative real if parallel or a positive real if anti-parallel; two vectors produce a vector if perpendicular; and ususally two vectors produce a real and a vector if not parallel or perpendicular!

This could open up a whole new fiedl of "particle Physics". The simple answer is the 4th dimension! The 4th dimension is a real dimension. This real dimension satisfies Closure. Two vectors produce a real and this is in the 4th real dimension. This dimension saves Closure because now the the elements are called quaternions. A quaternion is the sum of a real and three vectors, thus making four dimensions thus quater, Latin for 4.

If A and B are quaternions, then AB is a quaternion. Ths 4th dimesnsion has units like the three space dimensions - meters, r=ct is the fourth dimension where c is the speed of light and t is time. both c and t are real numbers and reals time reals gives reals. The speed of light c is a real number not a vector, thus the veclocity of light is wrong, because velocity denotes a vector not a real.

Man did not make the 4th dimension. You could say the 4th dimension was made when God said "Let there be Light!"

Quantum mechanics resolves the collapsing atom paradox by introducing the concept of superposition, where particles can exist in multiple states simultaneously until measured, and the wave function collapse occurs upon measurement. This means that an atom can exist in multiple states until an observation is made, at which point it assumes a definite state. This phenomenon is fundamental to the probabilistic nature of quantum mechanics.

There is no scientific evidence or documented case of human levitation. Levitation is often associated with magic, illusions, or myths, but there is no credible research supporting the idea that people can defy gravity and levitate.

Heisenberg, Dirac and Schrodinger all made large combinations. Schrodinger is famous for his wave mechanics, Heisenberg for his matrix notation. Dirac realised that the theories of Heisenberg and Schrodinger were essentially the same. He also created the Dirac equation, an important step in the creation of a relativistic version of Quantum Mechanics.

1. Solid sphere model
2. Planetary model
3. Quantum mechanical model

A laser beam is a coherent light source that emits a narrow beam of light due to the alignment of its waves. In contrast, light from a tube light is incoherent and emits light in all directions, resulting in a blurry appearance. The difference in coherence and directionality between laser light and tube light accounts for their distinct characteristics.

This principle is known as "Irreducible Complexity," which suggests that certain biological systems are too complex to have evolved from simpler, predecessor systems. It is often used as an argument against the theory of evolution.

No, sound in air cannot be polarized because sound waves are longitudinal waves in which the vibrations occur in the same direction as the wave propagation. Polarization is a property of transverse waves, where the vibrations are perpendicular to the direction of wave propagation.

No, metallic bonds have strong forces that hold metal atoms together in a lattice structure. These bonds are formed due to the attraction between the positively charged metal ions and the delocalized electrons.

The potential step is the barrier for particles to enter in to some region ,for example ,consider an electron with incident energy greater than the potential energy of an atoms ,will easily penetrate in to the atom an will comes out with some net changes in its energy and wave function ,

On other hand the electron having smaller energy than the potential of atom can not penetrates in to the atom ,it will bounces back from the atom ,

so here the neutral atom behaves as a potential step (barrier)

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That both photons AND electrons exhibit interference patterns when they have a choice of slits to go through, even if these particles leave the emitter and hit the detector one at a time. It is as if the particles are interfering with themselves.

The question I'll answer is "How is the Compton Effect best explained by the particle nature of light?"

When x-rays are sent into a metal, some of them are scattered out at an angle. When this happens, their wavelength changes, and this change depends on the angle at which they come out. Deriving this formula is VERY easy if we assume that the scattered x-rays are particles hitting an electron within the metal. It is impossible to do so by assuming the x-rays are simple EM waves with a very high frequency.

The profession of auto mechanics originated in the late 19th and early 20th centuries alongside the development of the automobile industry. Mechanics initially focused on maintaining and repairing early car models. Over time, as vehicles became more complex, the field evolved to encompass various specialties and disciplines within automotive technology.

Harmonic perturbation refers to a periodic external force or disturbance applied to a system that is close to its natural harmonic frequency. This perturbation can affect the behavior of the system, causing resonance or other dynamic responses that are not present in the absence of the perturbation. Understanding and analyzing harmonic perturbation is important in various fields such as physics, engineering, and biology.

Dimensions in general represent degrees of freedom in motion. That means each dimension adds one independent direction in which an object may move.

Additional dimensions beyond the 3 basic and 1 time dimension work in the same way. However I suspect the question originates from the added dimensions that string theory (and other theories) proposes.

In that case it is important to note that these additional dimensions are curled up in a complex structure known as a Calabi-Yau manifold. These structures are very small and therefore cannot be seen with the eye.

A good example given by Brian Greene in one of his books is that of a garden hose which has ants walking on it. The hose represents a two dimensional space, one in the direction of the hose, and one which moves the ant around it. Close up you can clearly see that you have these two degrees of freedom.

However if you move far away the hose will appear to be a line and the second (curled up) dimension appears to vanish. In the same way the curled up dimensions that string theory predicts are also invisible to the naked eye, although they might eventually be probed by particle collider experiments.

Electrons are not formed from energy quanta; they are elementary particles that exist as fundamental units of matter. However, electrons can be created in processes such as beta decay, where a neutron transforms into a proton, electron, and an antineutrino. These processes involve the conversion of energy into matter, following the principles of quantum mechanics.

Classical mechanics is the alternative to quantum mechanics. It is a branch of physics that describes the motion of macroscopic objects using principles established by Isaac Newton. Unlike quantum mechanics, classical mechanics assumes that objects have definite positions and velocities at all times.

There is no reasonable alternative to quantum mechanics, at least not something that can even compare with the predictive power and experimental accuracy as quantum theory. If you want to make predictions about things happening at small scales you cannot do without quantum mechanics.

Also note that certain models which are now considered as possible theories of everything (e.g. string theory) all expand upon quantum mechanics, they do not make quantum mechanics invalid or unnecessary.

The merger of quantum mechanics with the special theory of relativity is commonly known as quantum field theory. According to this theory every particle of matter is just an excitation of a field that is everywhere in space. There is a different field for every different particle (this is not really true, but close enough).

You might already be familiar with electromagnetism. In that theory (which has now been completely absorbed into quantum field theory) electric and magnetic forces are transmitted via photons. These photons are just excitations of the photon field.

A photon has no mass, but all particles can be thought as as being excitations of fields. There is for example an electron field, but also a neutrino field and a muon field.

In the dirac view of quantum mechanics, operators are the center of analysis. An operator is some mathematical operation that acts on the wavefunction (psi) which returns an observable. Lets look at some examples:

say psi=exp(ik(dot)r)*exp(iomega*t) (which is the case for a free particle)

the momentum operator is the -ihbar gradiant applying this to our psi- we get hbar k. This is called the observable.

perhaps more familiar the energy operator which would likewise return hbar omega. Now doesn't that look familiar!

Interestingly enough, these two examples point out that the conservation of momentum and energy stem from the laws of physics being invariant, regardless of position and time.

Math Prelude:

Orthogonal wave functions arise as a natural consequence of the mathematical structure of quantum mechanics and the relevant mathematical structure is called a Hilbert Space. Within this infinite dimensional (Hilbert) vector space is a definition of orthogonal that is exactly the same as "perpendicular" and that is the natural generalization of "perpendicular" vectors in ordinary three dimensional space. Within that context, wave functions are orthogonal or perpendicular when the "dot product" is zero.

Quantum Answer:

With that prelude, we can then say that mathematically, the collection of all quantum states of a quantum system defines a Hilbert Space. Two quantum functions in the space are said to be orthogonal when they are perpendicular and perpendicular means the "dot product" is zero.

Physics Answer:

The question asked has been answered, but what has not been answered (because it was not was not asked), is why orthogonal wave functions are important. As it turns out, anything that you can observe or measure about the state of a quantum system will be mathematically represented with Hermitian operators. A "pure" state, i.e. one where the same measurement always results in the same answers, is necessarily an eigenstate of a Hermtian operator and any two pure states that give two different results of measurement are necessarily "orthogonal wave functions."

Conclusion:

Thus, there are infinitely many orthogonal wave functions in the set of all wave functions of a quantum system and that orthogonal property has no physical meaning. When one identifies the subset of quantum states that associated pure quantum states (meaning specifically measured properties) and then two distinguishable measurement outcomes are associated with two different quantum states and those two are orthogonal. But, what was asked was a question of mathematics. Mathematically orthogonal wave functions do not guarantee distinct pure quantum state, but distinct pure quantum states does guarantee mathematically orthogonal wave functions. You can remember that in case someone asks.

The smallest particle in quantum physics is typically considered to be the quanta of energy known as a photon, which is a fundamental particle that carries electromagnetic radiation. However, there are also other elementary particles such as electrons, quarks, and neutrinos that are considered fundamental building blocks of matter.

The speed of light was predicted before it was ever measured. If you write the

differential equation of a wave, there's a very definite place in the equation where

the speed of the wave appears.

The Scottish Physicist James Clerk-Maxwell took four equations of electricity and

magnetism that had been discovered by earlier scientists, and succeeded in

mashing them together to come up with the equation of an electromagnetic wave.

Right there in the spot where the wave speed should be was the quantity

[ (electrostatic permittivity of space) x (magnetic permeability of space) ] .

Both of those properties of space had been kind-of measured by Maxwell's time,

but now it suddenly became very urgent to go back and work on measuring them

with the utmost accuracy ... and at the same time, to figure out a way to measure

the speed of light. Because if that quantity could be shown to match the real speed

of light, then we would know that light is an electromagnetic wave, and that Maxwell's equation for it is an accurate mathematical description of it.

You asked "Why is that the speed of light ?" The answer is: Because light is an

electromagnetic wave, therefore its speed is determined by those two properties

of free space, and the values of those two properties of space happen to be

such and such."

Now, we can almost hear you asking "Why are the values of those two characteristics

of space the numbers that they are, and not a bit more or less ?"

All we can tell you is that there are cosmologists who are actually working on that

esoteric question, along with the question of why other properties of the universe (For example, the gravitational constant.) are the numbers that they are. One realization that has emerged is the fact that if a few of the constant numbers of nature were just slightly different from what they actually are, then life would not be possible.

As the wavelength increases to infinity the electro-magnetic continuum take on a new base value and with no variation has no radiation to transmit.

As the wavelength decreases to zero the energy packet become a massive body and therefore is no longer a radiating.