Quantum Mechanics for Beginners
Introduction to Quantum Mechanics
RNfinity | 04-03-2023Introduction to Quantum Mechanics
The majority of quantum mechanics development occurred in the first half of the twentieth century. It is focused on the smallest particles with their characteristics, the microphysical objects and quantities. The smallest quantum mechanical particles are invisible to the human eye. Hence, it is impossible to experience a quantum system with our senses. Particularly, quantum mechanics defies the accepted theory that nature is always being generated and quantifiable.
Quantum mechanics (QM) is study of
physics on extremely short length scales, though it also directly applies to
some macroscopic systems. The word "quantum" refers to
the notion that certain quantities can only have discrete values in quantum
physics, as opposed to classical mechanics. Nonetheless,
some quantities continue to have continuous values [1].
A Brief History of QM
Particles in quantum
physics exhibit wavelike characteristics, and the Schrodinger equation, a
specific wave equation, determines how these waves behave. It is a mathematical
representation of the probability of finding a particle in a particular
location. This is contrary to the classical physics interpretation of reality, where
matter is made of particles, which are discrete objects that behave in a
predictable way and have specific, determinable locations.
Let's briefly review
the development of quantum mechanics throughout time.
Max Planck:
Max Planck
hypothesized in 1900 that energy-rich quantized lumps of light with frequency v
are released in integral multiples of the quantity.
E = hν
Albert Einstein:
According to Albert Einstein in 1905, the quantization
is a property of light, and the lumps can be thought of as particles that we
now refer to as "photons." His research on the photoelectric effect,
which deals with how light is absorbed by a material and how it emits
electricity, led to this suggestion.
E = ℏω
Niels Bohr:
According to Niels Bohr in 1913, atoms' electrons
exhibit wave-like characteristics. A few aspects of hydrogen were successfully
explained by this, including the known quantized energy levels.
Louis de Broglie:
According to Louis de
Broglie in 1924, all particles are connected to waves, with the frequency and
wavenumber of the wave being determined by the same relationships that we
discovered for photons above, namely E = ℏω, p= ℏk. The so-called wave particle duality results from the fact that every
particle has a wave attached to it.
Werner Heisenberg:
Matrix mechanics was
incorporated into Werner Heisenberg's formulation of quantum mechanics in 1925.
Instead of discussing this matrix formulation, we will examine the wave
formulation that follows that was proposed by Schrodinger.
Erwin Schrodinger:
A wave-based interpretation of quantum mechanics was
developed by Erwin Schrodinger in 1926. He recorded a wave equation (known as
the Schrodinger equation) that describes how waves change through time and
space.
Max Born:
Max Born accurately identified the probability
amplitude in Schrodinger's wave. To get the desired probability, the wave must
be squared, which is what we mean by "amplitude." More specifically,
we must square the absolute value of the wave because it is inherently
complicated. This results in the probability of discovering a particle at a
specific location.
Paul Dirac:
Paul Dirac demonstrated that the interpretations of
quantum mechanics proposed by Heisenberg and Schrodinger were similar in the
sense that they might both be obtained from a more general interpretation of
the theory.
John Bell:
Bell's Inequality (1964): In 1964, John Bell proposed
a way of testing whether particles were truly "entangled," or linked,
such that the state of one particle is immediately affected by the state of
another, regardless of the distance between them, or whether their properties
were inherent at their moment of generation and behaved in accordance with
Einstein, Podolsky, Rosen hidden variables explanation.
Due to the fundamental differences between the
physical principles of quantum mechanics and those of classical mechanics,
it is commonly considered as new branch of
physics [2]. Superposition, entanglement, and quantum teleportation
all work differently than we are accustomed to thinking about them in our
Newtonian world. Even Einstein had
trouble describing this fact, implying to entanglement as "spooky activity at a
distance" [1], and it is impossible to envisage
explanations like Schrödinger's cat [3]. Richard Feynman, a scientist,
pioneered the idea of quantum computation by arguing that computers may apply
the fundamental ideas of quantum mechanics to solve quantum mechanical issues.
Quantum computers have
also been possible due to the shrinking size of computer parts. It is expected
that components the size of a single atom will exist. Here, quantum mechanics
is required since the laws of classical physics are no longer relevant [4].
The amount of information amassed regarding
the field of quantum mechanics has greatly increased in recent years.
Nonetheless, many people find it difficult to begin studying quantum mechanics.
The principles and their implications are challenging to understand. As quantum
computers become more prevalent, more people may be required to study quantum computer programming, which calls for
deep knowledge of quantum physics. The quantum circuits which are core of many quantum computers, have been the
subject of countless attempts in the past. Since games engender an engaging approach, several of them employ game theory
and contests to establish an
easy and interesting entrance point to
quantum computing [5].
It is becoming more and more important, to study quantum computing because of
the great progress and potential of this technology [6].
According to Nita et al. [6], quantum literacy has to be made more
approachable for a variety of students. According to Stadermann et al. [6], who investigated the secondary education
quantum physics curricula of 15 different countries, quantum physics and
quantum mechanics are being introduced earlier and earlier. They also see the
opportunity to have "unusual" discussions about this difficult
subject. Perhaps children who
play quantum games as they grow up may develop an instinctively
grasp of quantum phenomena that our young people
lack.
Quantum computers cannot employ the boolean
algebra logic of conventional computers because of quantum mechanics. A
conventional computer uses bits, and binary
state with two possible values, to perform calculations. These variables could be categorised as active or inactive, true or
false. Yet, the most common ways to express them are as 1 or 0. A quantum
computer, in contrast, runs on concept of "qubits," or "quantum
bits." Instead of adopting a single state of 1 or 0, a qubit, unlike a
normal bit, adopts a true combination
of these states. "Superposition" is another
name for this orderly collection of states.
In some varieties of quantum computers,
quantum gates are applied to these qubits as fundamental operations. Quantum
gates are not devices, in contrast to digital gates. These could be considered
changes to the state of a qubit (spin). This process alters a qubit's ground
state.
A quantum circuit is
made up of numerous quantum gates used in succession. It could be viewed as a
particular type of computer programs that describes several manipulations of
the fundamental states of various qubits.
Rules to understand
quantum mechanics:
When viewed across the
lens of Newtonian universe, quantum mechanical phenomena are challenging to
understand. The three following rules are of the vital importance:
Superposition:
A capacity of quantum
particle to coexist in multiple states at once with differing probabilities. For
example, a particle can exist in two different locations at the same time, or may
have two different energy levels simultaneously.
This idea was famously
illustrated by Schrödinger's cat experiment, in which a hypothetical cat is
placed in a box with a vial of poison that will be released if a radioactive
particle decays. According to quantum mechanics, until the box is opened, and
the observer looks inside, the cat exists in a superposition of both being alive
and dead.
Entanglement:
It is a process in
which far elements of a quantum system show mysterious relationships. In this
case, status of one component affects the state of another component. This
means that if the properties of one particle are measured, then the properties
of the other particle can be determined immediately, even if the particles are
separated by vast distances.
This phenomenon was
famously described by Einstein as "spooky action at a distance," and
it has been demonstrated in many experiments.
Quantum Uncertainty
One of the core
principles of quantum mechanics is the uncertainty principle. The uncertainty
principle states that the position and momentum of a particle cannot both be
known with absolute certainty. The more precisely one is known, the less
precisely the other is known.
Collapse:
The method through
which quantum states of system are transformed into classical states. Collapses
happen when we evaluate quantum circuit and so make system smaller. It is
crucial to understand that measurement alone can determine the state of qubits.
A base state of |
0> or | 1> results from state’s collapse at this point. This procedure
destroys the qubit's state, which can only be restored by retrying quantum
gates in original way [7].
Applications of
Quantum Mechanics
While the principles
of quantum mechanics may seem abstract and theoretical, they have many useful technological
applications. One of the most well-known applications is the laser, which
relies on the principles of quantum mechanics to produce a focused beam of
light. Other applications include quantum cryptography, which uses the
principles of entanglement to create secure communication channels, and quantum
computing, which uses the principles of superposition and entanglement to
perform complex calculations much faster than classical computers.
Quantum information Processing
Quantum information
processing makes extensive use of key aspect of quantum mechanics. Superposition
states:
Compared to their
classical counterparts, quantum systems have far deeper and more intriguing
reality. A single bit, the most fundamental component of any traditional
information processor, can only exist in one of two potential states: 0 or 1. A
single quantum bit, or qubit, has access to an infinite number of such
superposition states. In a similar fashion to how a musical note has several
harmonic frequencies, nature permits it to simultaneously have a component that
corresponds to 0 and a part that corresponds to 1.
Information technology
and quantum mechanics
There are two ways
that information technology (IT) can benefit from quantum physics, which might
be loosely categorised as evolutionary and revolutionary. Both of which are very
active research fields with huge technological potential. When quantum physics
is used as a tool in evolutionary research, a significant portion of its impact
can be understood and appreciated without having a firm grasp of the theory
itself. Paradoxically, quantum mechanics plays an enormous role in
revolutionary work.
Quantum physics is fundamentally
working in evolutionary IT work to better comprehend and thereby enhance
existing technologies. For example, understanding a quantum behavior of
electrons in a materials is beneficial for the creation of lesser and quicker
silicon or other semiconducting devices. The switch to superconducting
Josephson junction devices from silicon transistors would be a little more
radical. Superconductors may be naturally quantum in nature, but this would not
create a fundamentally new technology. Here, faster digital switching and less
energy use would be advantages of superconducting.
Nonetheless, the
logical operations carried out and the physical bits that are manipulated in such
devices are identical to those of other devices. These well-known logical
processes continue to follow the same classical physics laws as they have
always done. If quantum physics has an additional, very distinct effect on
information technology, then a truly radical revolution occurs. Consider
machines that genuinely process information and conduct logical operations in
accordance with quantum physics rather than improved copies of what we already
have. Such devices, which would be a component of the emerging quantum
information technology (QIT), are significantly different from their classical
counterparts [8].
Fundamental particles
like electrons, in contrast to billiard balls, can display interference
phenomena that resemble waves, and two of them can become entangled. Similarly,
machines that store, analyse, and transfer information in a quantum mechanical
manner are able to perform tasks with that information that would seem
completely uncharacteristic or even impossible for classical machines. However,
it is not that simple; if it were, QIT would have been in existence for
considerable amount of time by now. The issue is that detecting electrons
usually causes them to move around, destroying entanglement and interference.
In mathematics, the
state of quantum particle is often indicated by |Ψ>) is a vector in an
abstract Hilbert space of potential states for system. A basis made up of
the two potential classical states, |0> and |1>, spans a space for single
qubit. With the right selection of the complex coefficients a and b, each state
of a qubit could be reduced into superposition.
|Ψ> = a|0> + b|1>
In this case, |Ψ>
is represented by vector, which is an orthogonal 2D unit vector used in a
common representation of the basis ( 01) and (10) [9].
Quantum mechanics of
today
The development of
quantum mechanics led to the Nobel Prize in Physics being awarded to Planck,
Einstein, Bohr, and many others. But if they were still living today, they
wouldn't recognize the world today, which has changed as a result of there
discoveries. Quantum mechanics runs computers due to transistors.
Transistors are little electronic components found within computers that serve
as data storage. A transistor conducts electricity when it is turned on, and
the computer interprets this as a "1." A transistor stops conducting
electricity when it is turned off, and the computer interprets this as a
"0." Ones and zeros are the language of computers. To encrypt data,
they turn transistors on or off. A semiconductor substance is used to create
transistors. According to quantum mechanics, an electron can only occupy a
limited range of energy levels. These levels are "bands," or ranges
of permitted energy values, when examining a big group of electrons, such as
those present in semiconductors [10].
The semiconductor
conducts electricity when it is linked to a voltage that is within the energy
band. It does not conduct electricity when attached to a voltage that is
outside of the permitted energy band. As an insulator, it works. Transistors
turn on or off in this manner, which the computer interprets as a 1 or 0. Digital
refers to anything that operates using a binary code of 1s and 0s.
Semiconducting transistors are used in almost every digital device you can
imagine. even your television, as well as your computer and mobile device!
Think of a world without these items or the Internet. This would be world
without quantum mechanics.
The Future of Quantum
Mechanics
As technology
continues to advance, it is likely that our understanding of quantum mechanics
will also continue to develop. New experiments may shed light on some of the
remaining mysteries of quantum mechanics, and lead to new applications and
technologies that we can't even imagine yet.as an example, scientists are
exploring the possibility of using quantum entanglement for faster-than-light
communication, or even for teleportation.
Conclusion
Quantum mechanics has
fundamentally changed our understanding of the universe. While it may seem
daunting at first, with patience, anyone can begin to grasp the basic concepts
of quantum mechanics. With further progress, many new technologies and insights
that could revolutionize the world as we know it, may be around the corner.
Reference
[4] S. Gudder,"Spooky Action at a Distance," arXivpreprint arXiv:2005.11870, 2020.
[8] A. Barenco et al., Introduction To Quantum Computation And Information. WorldScientific, 1998.