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Quantum Mechanics

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- Particle and wave duality
This postulates that all matter exhibits both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects.

- For complete knowledge of matter duality, one must have concepts of Compton effect, photoelectric effect,de Broglie wavelength, and Planck's formula for black-body radiation. All these effects and theories proves the dual nature of matter.
- There are different experiments for light set by scientists proves that light have dual nature i.e. particle as well as wave nature... In 1901, Max Planck published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an
*ad hoc*mathematical assumption of quantized action of the oscillators (atoms of the black body) that emit radiation. It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized into photons.

This is one of the most difficult aspects of quantum systems to understand.

What we feel is reality

In the everyday world, it is natural and intuitive to think of everything (every observable) as being in a define state. Everything appears to have a definite position, a definite speed, a definite weight, and a definite time of being there.

What quantum experiments tell us

However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum (speed) or its energy and time (since they too are conjugate pairs); rather, it provides only a range of probabilities in which that particle might be given its position and momentum (speed) probability.

The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wave functions become entangled, so that the original quantum system ceases to exist as an independent entity.

Wave Function

In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a

**probability distribution**for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. This is called the**wave function**.Wave function collapse

If one measures the observable, the wave function will instantaneously be an defined state of that observable. This process is known as

**wave function collapse.**Probabilistic

*The probabilistic nature of quantum mechanics is linked to the act of measurement.*Quantum Theory

a subset of physics explaining the physical behaviours at the molecular, atomic and sub-atomic levels

- Quantum Theory
Matter and radiation on the atomic scale's behavior seems peculiar, and the consequences of quantum theory are so difficult to comprehend and also to believe. Its concepts and notions based on observations of the world conflict. There isn't any reason, however, why the behaviour of the universe should comply with the way we want our world to behave.

Key facts derived from quantum theory

- it is generally impossible, even in principle, to measure a system without disturbing it.
- both radiation and matter have characteristics of particles and waves.
- objects exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B.

Quanta

a quantum (plural: quanta) is the minimum amount of any physical entity involved in an interaction. This means that the magnitude of the physical property can take on only certain discrete values.

Quanta

Quanta is like butter blocks

Quantum comes from quantum, which means small quantity. Until the beginning of the twentieth century, physical notions were continuous notions. Continuous means that you can send an object with a speed of 150 kilometers per hour, 151, 150.5, 150.45 or 150.9999999, in short all the values you want. Same for heat, temperature, conductivity, force, etc. Now a series of observations of phenomena obliged physicists to consider that in the world of particles, on a tiny scale, there are

**notions which are not continuous and make little jumps of value**, such as flea jumps .To make an analogy, say that in the creamer you can buy a continuous value of butter (for example 147.52 grams) whereas in the

**quantum world, you are, as in the grocer, forced to buy by blocks of 250 or 500 grams.**As these notions make jumps, one speaks of quantum phenomenon, "which makes jumpsQuanta can not apply

to the speed of a car

**In classical physics**, when you drive, you can go from 0 km / h to 50 km / h with your car,**you pass through all the intermediate speeds**: 1 km / h, 2 km / h, 3 km / h, but also 1.1 km / h 1.2 km / h and so on. Take any number with a comma between 0 and 50 and there is a moment when you will have passed through this speed.**In quantum physics, this is no longer true**. You would go**directly from 0 km / h to 20 km / h**then from 20 km / h to 50 km / h. The transition is instantaneous. Mathematically, it will be noted that the acceleration undergone is then infinite,**which makes it impossible**to still be alive driving your quantic car ...Each speed value is then a possible speed level and said "authorized". The other values for speed are called "prohibited". It is impossible to go at a speed of 1 km / h, 10 km / h or 21 km / h. Only values of 0 km / h, 20 km / h and 50 km / h are possible in this example.

**Quantum physics**works exactly this way. Not with speeds and cars but rather with energy levels and particles:**one particle can have different levels of energy allowed, the others being all prohibited**. An electron can in fact**pass from one level of energy to another instantaneously**, without passing through all the intermediate levels.Quantization

The

**concept of quantization**of radiation was discovered in 1900 by**Max Planck**, who had been trying to understand the emission of radiation from heated objects, known as black-body radiation. By assuming that**energy can only be absorbed or released in tiny, differential, discrete packets**he called "bundles" or "energy elements", Planck accounted for certain objects changing colour when heated.On December 14, 1900,

**Planck**reported his findings to the German Physical Society, and introduced the**idea of quantization**for the first time and deduced the numerical value of h, known as the**Planck constant.**After his theory was validated, Planck was awarded the**Nobel Prize**in Physics for his discovery in 1918.A new model of the Atom

In 1913

**Niels Bohr**proposed a new model of the atom that included**quantized electron orbits**: electrons still orbit the nucleus much as planets orbit around the sun, but they are only permitted to inhabit certain orbits, not to orbit at any distance. When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead,**the electron would jump instantaneously from one orbit to another**, giving off the emitted light in the form of a photon. The possible energies of photons given off by each element were determined by the differences in energy between the orbits.Max Plank

The quantum principle states that no experiment can measure an action smaller than ℏ (Plank Constant). In nature, action values smaller than ℏ = 1.06 ⋅ 10−34 Js are not observed.

- Max Plank constant
**In nature, action values smaller than ℏ = 1.06 ⋅ 10−34 Js are not observed.**The fundamental constant ℏ, which is pronounced ‘aitch-bar’, is called the

**quantum of action**, or alternatively Planck’s constant. Planck discovered the quantum principle when studying the properties of incandescent light, i.e., of light emanating from hot bodies.All attempts to observe physical action values smaller than this fail. In other words, in nature – as in a good cinema film – there is always some action.

**The existence of a smallest action value is the so-called quantum principle.**When Planck saw that the quantum of action allowed defining all units in nature, he was as happy as a child; he knew straight away that he had made a fundamental discovery, even though (in 1899) quantum theory did not yet exist. He even told his seven-year-old son Erwin about it, while walking with him through the woods around Berlin. Planck explained to his son that he had made a discovery as important as universal gravity. Indeed, Planck knew that he had found

**the key to understanding many of the effects that were then unexplained**.Quantum effects surround us on all sides. However, since the quantum of action is so small, its effects on motion appear mostly, but not exclusively, in microscopic systems. Quantum theory is the description of microscopic motion.

**Quantum theory is necessary whenever a process produces an action value of the order of the quantum of action.**Therefore, a smallest action implies that there is a smallest change value in nature.

**If we compare two observations, there will always be change between them.**Any system whose indeterminacy is of the order of ℏ is a quantum system; if the indeterminacy product is much larger, the system is classical, and then classical physics is sufficient for its description. So even though classical physics assumes that there are no measurement indeterminacies in nature, a system is classical only if its indeterminacies are large compared to the minimum possible ones !

In other terms, quantum theory is necessary whenever we try to measure some quantity as precisely as possible. In fact, every measurement is itself a quantum process. And the indeterminacy relation implies that measurement precision is limited. In other words, the microscopic world is fuzzy

Randomness – a consequence of the quantum of actionWhat happens if we try to measure a change smaller than the quantum of action? Nature has a simple answer: we get random results. If we build an experiment that tries to produce a change or action of the size of a quarter of the quantum of action, the experiment will produce, for example, a change of one quantum of action in a quarter of the cases, and no change in three quarters of the cases,* thus giving an average of one quarter of ℏ.

⊳ Attempts to measure actions below ℏ lead to random results.

If you want to condense quantum physics in one key statement, this is it.

The quantum of action leads to randomness at microscopic level. This connection can be seen also in the following way. Because of the indeterminacy relations, it is im-possible to obtain definite values for both the momentum and the position of a particle.

Obviously, definite values are also impossible for the individual components of an experimental set-up or an observer. Therefore, initial conditions – both for a system and for an experimental set-up – cannot be exactly duplicated. The quantum of action thus implies that whenever an experiment on a microscopic system is performed twice, the outcomes will (usually) be different. The outcomes could only be the same if both the system and the observer were in exactly the same configuration each time. However, because of the second principle of thermodynamics, and because of the quantum of action, reproducing a configuration is impossibleObviously, there will be some average outcome; but in all cases, microscopic observations are probabilistic. Many find this conclusion of quantum theory the most difficult to swallow. But fact is: the quantum of action implies that the behaviour of quantum systems is strikingly different from that of classical systems. The conclusion is unavoidable:

⊳ Nature behaves randomly

If the quantum of action is the smallest observable change in a physical system, then two observations of the same system must always differ. Thus

**there cannot be perfect rest in nature.**Not only does the quantum of action prevent the existence of rest;

**the quantum of action also prevents the observation or measurement of rest**. In order to check whether an object is at rest, we need to observe its position with high precision. Because of the wave properties of light, we need a high-energy photon: only a high-energy photon has a small wavelength and thus allows a precise position measurement. As a result of this high energy, however, the object is disturbed. Worse, the disturbance itself is not precisely measurable; so there is no way to determine the original position even by taking the disturbance into account. In short, perfect rest cannot be observed – even if it existed.The quantum of action implies that rest is impossible in nature. In fact, even at extremely low temperatures,

**all particles inside matter are in motion.**

Light as Photon

Light is made of photons. The smallest possible illumination is due to a single light particle. Today, these particles are called photons

- Light and Photons
The concept of a photon is indeed necessary for a precise description of light; but the properties of photons are unusual and require a change in our habits of thought.

Influenced by Newton, most physicists of the 18th century believed that light consisted of particles, which they called corpuscles.

All experiments thus show the same result : whenever sensitive light detectors are constructed with the aim of ‘seeing’ as accurately as possible – and thus in environments as dark as possible – one finds that light manifests as a stream of light quanta. Nowadays they are usually called photons, a term that appeared in 1926.

The everyday continuum description of light is similar in many respects to the description of water as a continuous fluid: photons are the atoms of light, and continuity is an approximation valid for large numbers of particles

The photography proof of the existence of photons

A simple way is to start with a screen behind a prism illuminated with white light. The light is split into colours. As the screen is placed further and further away, we use some black-and-white photographic film. Film is blackened by daylight of any colour; it becomes dark grey at medium intensities and light grey at lower intensities. Looking at an extremely light grey film under the microscope, we discover that, even under uniform illumination, the grey shade is actually composed of black spots, arranged more or less densely. All these spots have the same size. This regular size suggests that a photographic film reacts to single photons.

The Photo electric proof of existence of photons

the photoelectric effect is usually cited as the first and most obvious experimental proof of the existence of photons. In 1887, Heinrich Hertz observed that the light causes emission of electrons, and that the energy of the ejected electrons does not depend on the intensity of the light, but on its frequency.

in 1905, Albert Einstein deduced the measurements from the assumption that light is made of photons of energy. He imagined that this energy is used partly to take the electron over the threshold, and partly to give it kinetic energy. More photons only lead to more electrons, not to faster ones. In 1921, Einstein received the Nobel Prize for the explanation of the photoelectric effect.

Where is a photon when it moves in a beam of light?

Quantum theory gives a simple answer: nowhere in particular. This is proved most spectacularly by experiments with interferometers. Interferometers show that even a beam made of a single photon can be split, led along two different paths, and then recombined. The resulting interference shows that the single photon cannot be said to have taken either of the two paths. If one of the two paths is blocked, the pattern on the screen changes. In other words, somehow the photon must have taken both paths at the same time.

**Photons cannot be localized: they have no position**

What are the carecteristics of a photon ?

photons have no measurable mass and no measurable electric charge.

a photon has zero size.

Photons cannot be localized: they have no position

it is impossible to measure both the momentum (ie speed) and the position of a photon.

intense light can push objects

light is a stream of photons. It is indeed a ‘luminary movement of luminous bodies’.

photons somehow ‘turn’ – in a direction either parallel or antiparallel to their direction of motion. this is called the spin of a photon

A particle with zero size cannot have any constituents. Thus a photon cannot be divided into smaller entities: photons are not composite. For this reason, they are called elementary particles

How can we count photons without destroying them?

One way is to reflect photons in a mirror and measure the recoil of the mirror. It seems almost unbelievable, but nowadays this effect is becoming measurable even for small numbers of photons.

Another way of counting photons without destroying them involves the use of special high-quality laser cavities. It is possible to count photons by the effect they have on atoms cleverly placed inside such a cavity.

In summary

In summary, light is a stream of photons. A single photon is the smallest possible light intensity of a given colour. Photons, like all quantons, are quite different from everyday particles. In fact, we can argue that the only (classical) particle aspects of photons are their quantized energy, momentum and spin. In all other respects, photons are not like little stones. Photons move with the speed of light. Photons cannot be localized in light beams. Photons are indistinguishable. Photons have no mass, no charge and no size.

Light as Wave

*Light behaves like waves, as*Interference is a result of the space-time propagation of waves- Light as Wave
Only after people had accepted that light is a wave, and then discovered and understood that quantum particles are fundamentally different from classical particles, was the quanton description successful.

Obviously, all electromagnetic fields are made of photons. At present, photons can be counted for gamma rays, X-rays, ultraviolet light, visible light and infrared light. However, for lower frequencies, such as radio waves, photons have not yet been detected.

Interference is a result of the space-time propagation of waves; photons appear only when interaction with matter takes place. The description of space-time propagation and the particle picture are mutually exclusive – this is one aspect of the complementary principle.The quantum of action implies that all waves are streams of quantons. In fact, all waves are correlated streams of quantons. This is true for light, for any other form of radiation, and for all forms of matter waves.

The indeterminacy relations show that even a single quanton can be regarded as a wave; however, whenever it interacts with the rest of the world, it behaves as a particle.

Interference is only possible if one cannot know where the detected photon comes from. The quantum mechanical description of the field in a situation of interference never allows ascribing photons of the superposed field to one of the sources. In other words, if it is possible to say from which source a detected photon comes from, interference cannot be observed.

The double split experiment proof of Light as wave

If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern in which the light is spread out.

in a double split experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The results are bright and dark bands on the screen — a result that would not be expected as our classical way of thinking would tell us we should expect to see 2 bight bands (and not seven).

This experiments tells us about the wave nature of light causes the light waves passing through the two slits to interfere, producing seceral bright and dark bands on the screen.

Superposition

- Quantum superposition
Quantum superposition refers to the quantum mechanical property of solutions to the Schrödinger equation. Since the Schrödinger equation is linear, any linear combination of solutions to a particular equation will also be a solution of it. This mathematical property of linear equations is known as the superposition principle. In quantum mechanics such solutions are often made to be orthogonal, such as the energy levels of an electron. By doing so the overlap energy of the states is nullified, and the expectation value of an operator (any superposition state) is the expectation value of the operator in the individual states, multiplied by the fraction of the superposition state that is "in" that state.

Wave Function

*Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The wave function is a mathematical description of these probabilities.*- Wave Function
A wave function or wave function is a mathematical tool in quantum mechanics that describes the quantum state of a particle or system of particles. It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where |ψ|

^{2}is equal to the chance of finding the subject at a certain time and position.- For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.
- In solving homework problems involving the wave function, familiarity with complex numbers is a prerequisite. Other prerequisites include the math of linear algebra, Euler's formula from complex analysis and the bra-ket notation.

Exemple of a wave function

Wavefunctions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The brighter areas represent a higher probability of finding the electron.

Uncertainty

The uncertainty principle states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision.

- Uncertainty
In quantum physics, a particle is described by a wave packet, which gives rise to this phenomenon. Consider the measurement of the position of a particle. It could be anywhere. The particle's wave packet has non-zero amplitude, meaning the position is uncertain – it could be almost anywhere along the wave packet. To obtain an accurate reading of position, this wave packet must be 'compressed' as much as possible, meaning it must be made up of increasing numbers of sine waves added together. The momentum of the particle is proportional to the wave number of one of these waves, but it could be any of them. So a more precise position measurement – by adding together more waves – means the momentum measurement becomes less precise (and vice versa).

We live in a classical world, where everything is based on quantum laws but nothing resembles the quantum world.

Christophe Galfard, The Universe in Your Hand: A Journey Through Space, Time, and Beyond

“When left alone, quantum particles behave as multiple images of themselves (as waves, really), simultaneously moving through all possible paths in space and time. Now, again, why do we not experience this multitude around ourselves? Is it because we are probing things around us all the time? Why do all experiments that involve, say, the position of a particle make the particle suddenly be

*somewhere*rather than everywhere? No one knows. Before you probe it, a particle is a wave of possibilities. After you've probed it, it is somewhere, and subsequently it is somewhere for ever, rather than everywhere again. Strange, that. Nothing, within the laws of quantum physics, allows for such a collapse to happen. It is an experimental mystery*and*a theoretical one. Quantum physics stipulates that whenever something is there, it can transform into something else, of course, but it cannot disappear. And since quantum physics allows for multiple possibilities simultaneously, these possibilities should then keep existing, even after a measurement is made. But they don't. Every possibility but one vanishes. We do not see any of the others around us. We live in a classical world, where everything is based on quantum laws but nothing resembles the quantum world.”

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