Introduction to Quantum Mechanics

What is Quantum Mechanics?

In physics, quantum mechanics (also known as wave mechanics in some of its interpretations) is one of the main branches of physics that explains the behaviour of matter and energy. Its field of application is intended to be universal (overcoming difficulties), but it is in the world of small that its predictions radically diverge from the so-called classical physics.

Specifically, quantum mechanics is also considered the part of itself that does not incorporate relativity in its formalism, only as added by means of perturbation theory. The part of quantum mechanics that does incorporate relativistic elements formally and with various problems in relativistic quantum mechanics or, more precisely and powerfully, quantum field theory (which in turn includes quantum electrodynamics, chromodynamics and electroweak theory within the standard model) and more generally, quantum field theory in curved space-time. The only interaction that could not be quantified has been the gravitational interaction.

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Quantum mechanics is the basis of studies of the atom, nuclei, and elementary particles (relativistic treatment is already necessary) but also in information theory, cryptography, and chemistry. Quantum mechanics is the last of the great branches of physics. It begins at the beginning of the 20th century, at the moment when two of the theories that tried to explain what surrounds us, the law of universal gravitation and classical electromagnetic theory, became insufficient to explain certain phenomena.

The electromagnetic theory generated a problem when it tried to explain the radiation emission of any object in equilibrium, called thermal radiation, which is the one that comes from the microscopic vibration of the particles that compose it.

Origin of Quantum mechanics

It is within statistical mechanics that quantum ideas were born in 1900. Louis de Broglie proposed that each material particle has a wavelength, inversely associated with its mass, (he called it momentum), and given by its speed. The physicist Max Planck came up with a mathematical trick: that if in the arithmetic process the integral of these frequencies was replaced by a non-continuous sum, infinity was no longer obtained as a result, thus eliminating the problem and, in addition, the result obtained was consistent with what was later measured.

It was Max Planck who then hypothesized that electromagnetic radiation is absorbed and emitted by matter in the form of quanta of light or photons of energy using a statistical constant, which was called the Planck constant. Its history is inherent to the 20th century.,

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Planck’s idea would have remained many years only as a hypothesis if Albert Einstein had not taken it up, proposing that light, in certain circumstances, behaves as independent energy particles (light quanta or photons). It was Albert Einstein who completed the corresponding laws of motion in 1905 with what is known as the special theory of relativity, demonstrating that electromagnetism was an essentially nonmechanical theory.

Thus culminating what has been called classical physics, that is, non-quantum physics. He used this point of view called by him “heuristic”, to develop his theory of the photoelectric effect. He published this hypothesis in 1905 and was awarded the 1921 Nobel Prize. This hypothesis was also applied to propose a theory about specific heat.

The speeds of the constituent particles should not be very high, or close to the speed of light. Quantum mechanics breaks with any paradigm of physics up to that moment, with it is discovered that the atomic world does not behave as we would expect. The concepts of uncertainty, indeterminacy, or quantization are first introduced here. Furthermore, quantum mechanics is the scientific theory that has provided the most accurate experimental predictions so far, despite being subject to probability.

Quantum theory was developed in its basic form throughout the first half of the 20th century. The fact that energy is exchanged discreetly was highlighted by experimental facts such as the following, inexplicable with the “earlier” theoretical tools of classical mechanics or electrodynamics:

Black body radiation spectrum, solved by Max Planck with quantization of energy. The total energy of the black body turned out to take discrete rather than continuous values. This phenomenon was called quantization, and the smallest possible intervals between the discrete values are called quanta (singular: quantum, from the Latin word for “quantity”, hence the name quantum mechanics). The size of a quantum is a fixed value called the Planck constant, and it is worth: 6,626 × 10: joules per second.

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Under certain experimental conditions, microscopic objects such as atoms or electrons exhibit wave behaviour, as in interference. Under other conditions, the same species of objects exhibit a particle, corpuscular behaviour (“particle” means an object that can be located in a special region of Space), as in the dispersion of particles. This phenomenon is known as wave-particle duality.

The physical properties of objects with related histories can be correlated to an extent prohibited by any classical theory, to such an extent that they can only be accurately described if we refer to both at once. This phenomenon is called quantum entanglement, and Bell’s inequality describes its difference from ordinary correlation. The measures of Bell’s inequality violations were among the greatest quantum mechanics

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Explanation of the photoelectric effect, given by Albert Einstein, in which this “mysterious” need to quantify energy reappeared.
Compton effect.
The formal development of the theory was the work of the joint efforts of various physicists and mathematicians of the time such as Schrödinger, Heisenberg, Einstein, Dirac, Bohr and Von Neumann among others (the list is long). Some of the fundamental aspects of the theory are still being actively studied. Quantum mechanics has also been adopted as the theory underlying many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics.

The region of origin of quantum mechanics can be located in central Europe, in Germany and Austria, and in the historical context of the first third of the 20th century.

The modern world of physics is remarkably founded on two main theories, general relativity and quantum mechanics, although both theories seem to contradict each other. The postulates that define Einstein’s theory of relativity and quantum theory are unquestionably supported by rigorous and repeated empirical evidence. However, both resist being incorporated into the same coherent model.

Einstein himself is known to have rejected some of the demands of quantum mechanics. Despite being clearly inventive in his field, Einstein did not accept the orthodox interpretation of quantum mechanics such as the assertion that a single subatomic particle can occupy numerous spaces at the same time.

Einstein also did not accept the even more exotic quantum entanglement consequences of the Einstein-Podolsky- Rosen (or EPR) paradox, which demonstrates that measuring the state of a particle can instantly change the state of its bound partner, although the two particles can be at an arbitrary distance. However, this effect does not violate causality, since there is no possible transfer of information. In fact, there are quantum theories that incorporate special relativity – for example.

Why quantum?

Einstein gave a good explanation and analogy with real life about the meaning of the word quantum and quantum. In his book “The Physics, Adventure of Thought” he says that, for example, in a coal mine, production can vary continuously, if we accept any unit of measurement, however small it may be. In other words, we could say that 1 more granite of coal was produced than yesterday. What we cannot do is express the variation of personnel in a continuous way, it does not make sense to speak of the increase in personnel by 1.80 people, that is, the measure of the number of personnel is discrete and not continuous.

Another example, a sum of money can only vary from one to another, discontinuously. The minimum unit for money is the penny. We say then that certain magnitudes change in a continuous way and others in a discontinuous or discrete way, that is, by elementary quantities or steps that cannot be reduced indefinitely. These minimal and indivisible steps are called elemental quanta of the magnitude in question. It is evident that when the precision of how measurements of any type of magnitude are carried out, units that were considered indivisible cease to be indivisible and adopt an even lower value.

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In other words, certain quantities that are considered continuous may have a discrete nature. It is evident that when the precision of how measurements of any type of magnitude are carried out, units that were considered indivisible cease to be indivisible and adopt an even lower value. In other words, certain quantities that are considered continuous may have a discrete nature. It is evident that when the precision of how measurements of any type of magnitude are carried out, units that were considered indivisible cease to be indivisible and adopt an even lower value. In other words, certain quantities that are considered continuous may have a discrete nature.

In physics, certain magnitudes considered for many years as continuous, are actually composed of how many elementals. Energy is one of these magnitudes that when studying the phenomena of the world of atoms, it was detected that its nature was not continuous but discrete and that there is a minimal or elemental unit of energy. This was Max Planck’s discovery with which quantum theory begins.

Quantum used as a noun refers to the smallest amount of something that is possible to have. In the world of classical physics, there is a concept that all physical parameters such as energy, speed, and distance travelled by an object are continuous. To understand what this is about continuous, let’s think about the thermometer that measures the temperature, when we see that it increases by one degree, it actually increases first by a tenth of a degree and thus following before by a millionth of a degree, etc., etc.

That is to say, the process of temperature increase that we measure with the thermometer we say is continuous. Well in the world of quantum physics this is not so, specifically when Max Planck studied how radiation is produced from an incandescent body, His explanation was that the atoms that make up the incandescent body, when they released energy in the form of radiation, did so not continuously, but in small blocks that he called energy quanta.

The strange thing about this whole process or Planck’s explanation is that there are no intermediate positions, that is, there are no half-means or a quarter-way. It is as if in the case of the thermometer there was no fraction of a degree, simply the temperature that is at 20º suddenly goes up to 21º. We say strange because what common sense indicates is that the temperature of an object increases when it receives heat/energy; If the body is at 20º and I give it heat in a small amount, it will not be enough for it to increase by one degree to 21º, but for something to increase.

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In the quantum world, it is as if those small amounts are being stored somewhere without manifesting themselves in any way (without increasing body temperature), so that suddenly when the amount of heat transmitted reached a value such that the thermometer now shows itself an increase of 1º, marking 21º. What happened in between?. Well, that although it does not happen in the case of temperature it is only an analogy to understand, it is what actually happens in the quantum world.

All the particles that make up the physical universe must move in quantum jumps. A body cannot absorb or emit light energy in any arbitrary quantity but only as integer multiples of a basic quantity or quantum. Returning to the strangeness of these phenomena, let’s imagine for a moment another analogy: we are throwing stones in a calm water pool. Common sense given by the experience we accumulate over time tells us that doing this will produce ripples in the pond that are the product of the energy that the stone transmitted when falling into the water.

A quantum pond would behave differently, when throwing one or more stones nothing will happen, and suddenly without any connection between the cause (throwing stones) and the effect (waves are generated on the surface), the pond will begin to vibrate with waves, until suddenly it will calm down again, even though at that moment we are throwing stones. If all the stones are the same size, and thrown from the same height, they will deliver the same amount of energy to the water when falling. If that amount of energy turns out to be less than the quantum of energy.

I want to emphasize the strangeness of this phenomenon, drawing attention to the fact that the quantum is not a quantity that can be subdivided, that is, the concept of continuity loses significance, between 0 and the quantum there is nothing. They are states that nature does not allow. This is the essential characteristic of Planck’s discovery when studying the phenomena called black body radiation (a topic that will be developed later): there is a lower limit to the energy change (absorption or emission of energy in the form of light) that an atom can to experience.

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