Introduction
The matter is anything that has mass and occupies space. The matter is made of small particles. All things that we see are made of the small particles that are in matter, whether relatively small or extremely huge. It is very easy to study the behavior of such large bodies. We can know much about them at any time. We can tell their location, their speed, and momentum if they are in motion and can predict their next moves. The branch of physics that studies the behavior of such bodies is classical mechanics. After discovering that matter is made of small particles, scientists got the interest to study the characteristics of these small particles relative to the huge bodies that they constitute. They soon discovered that the applied laws in the study of the large bodies no longer hold for these micro-particles. We have said that matter is made of small particles. These particles are atoms. We also have smaller particles that make up the atom. These are the electrons, protons, and neutrons. Studies have revealed that there could be more sub-atomic particles, but the mentioned three are still enough for us to talk about quantum mechanics. For instance, one cannot use any one of the three Newton’s Laws of motion to describe the speed, momentum, and position of an electron. Scientists then looked for an alternative way. Quantum mechanics started to develop at that point. Generally, we can say that classical mechanics is concerned with large bodies while quantum mechanics is concerned with particles on a micro-scale.
The History of Quantum Mechanics
The main period that physicists developed quantum mechanics was between 1859 and around 1930. Fine-tuning developments have taken place thereafter but these physicists had worked on the principle part.
Even though the main particles that quantum mechanics focuses on these days are the subatomic particles, scientists had not discovered all of them by the time this subject started developing. J.J. Thompson discovered the electron about 112 years ago in 1897 while the discovery of the neutron was in 1932. It is then hard to understand that the background of quantum theory dates back to 1859. The theory of blackbody radiation kicks off the long journey to the development of quantum mechanics. Gustav Kirchhoff did this work. An object that absorbs all light that falls on it is a blackbody. It does not reflect any light so it appears black to the observer. The body emits heat perfectly. Kirchhoff demonstrated that energy (E) varies with temperature (T) with frequency (v).
Kirchhoff presented a big challenge to his colleagues to uncover what J was. In 1879, Stefan Josef projected that the entire energy released by a black body is proportional to temperature when raised to its fourth power. Ludwig Boltzmann followed him in 1884 making the same conclusion. He used Maxwell’s electromagnetic and thermodynamics theory. This resulted in Stefan-Boltzmann’s law. Still, Kirchhoff’s challenge was still a puzzle.
Wilhelm Wien suggested a way out for the Kirchhoff puzzle. This was in 1896. The problem worked only for small values of wavelengths. Rubens suggested to Plank the correct formula for Kirchhoff’s J function that fitted experimental evidence for all wavelengths in 1900. Plank then used it to make a unique step of assuming that energy is made of distinct portions – energy quanta. In 1901, Ricci and Levi-Civita developed absolute differential calculus, which aided the analysis of Plank’s proposal (O’Connor, and Robertson, 1996).
It further became clear when Einstein examined the photoelectric effect, which is the ejection of electrons from certain surfaces e.g. metal surface. In 1906, he concluded that energy is in form of quanta. They occur distinctly in multiples of the function ħv. ħ is the planks constant. It is the reduced constant. In 1924, Bose proposed that quanta exist in different states. At around the same time, Louis de Broglie noted that particles are also wave-like. They have the duality of light. In 1926, Schrödinger gave an equation for the hydrogen atom. This was the genesis of wave mechanics. A complete derivation of Plank’s constant was in 1929. The principle of uncertainty explains why it is hard to get the position of a particle and at the same time obtain its momentum. Dx Dp ≥ = h/2Ď€ where Dx shows the uncertainty in position and Dp represents uncertainty in momentum. Bohr confirmed that the space-time coordinates match. This was in 1927. Von Neumann put quantum theory into operator algebra in 1932.
Fundamentals of Quantum Mechanics
Quantum mechanics has the following basics; wave duality, discrete energy, position and momentum, quantum states, quantum numbers, wave amplitude, and wave function.
Wave duality is the property of a particle to behave both as a wave and a particle. Photons are quantum particles related to electromagnetic waves (“Quantum Mechanics”, par 7). These photons have a definite amount of energy. The energy depends on the frequency of the associated wave. The energy is given by E = hf.
The second one is discrete energy. The measure of energy in particles is not continuous. They do not take any value but take certain definite values. Here, energy is discrete in nature. Angular momentum of various systems only comes in whole numbers. These are multiples of h/2. They do not come in decimals or fractions.
Real numbers do not represent position and momentum in quantum mechanics as it is in classical mechanics. They are Hermitian linear operators acting in ket space. This will represent all possible situations of a system (Fitzpatrick, Pp 33).
Quantum states and numbers are parameters used to describe systems in quantum mechanics. States describe the position of a particle, for example, the orbital. Quantum numbers define quantities related to the state. Such quantities are electric charge, angular momentum, and energy. They can only have certain distinct values confined in the quantum system.
Wave amplitude and function are for describing states. Probability amplitude is an intricate number function of position. Its quantity is definite at any point in space.
Application of Quantum Mechanics
In solid-state physics, the Kronig-Penny model is for showing the way periodic arrays of potential wells provide bands of allowed states with gaps. This knowledge is important in making things such as diodes, LED, and transistors. These are important components of electronics today. Schrödinger equation in nuclear physics aids in calculating the trends in atomic numbers and decay rates. We find this very important in nuclear energy production, in medicine, and indifferent lab applications. In explaining the photoelectric effect, you do not need photons but perturbation theory and approximations are what you need. They are very important. State-vector notations in the No-Cloning theorem help in the processes of cryptography, teleportation, ad basic quantum computing (Orzel, par 8). In subjects such as chemistry, quantum chemistry explains many important aspects. For instance, it explains how different inorganic and organic compounds are bonded. This is by relating the various orbitals that exist in different atoms.
Works cited
Fitzpatrick, Richard. Quantum Mechanics.The University of Texas at Austin. n.d. Web.
O’Connor, J. John and Robertson, F. Edmund.A History of Quantum Mechanics. www-history.mcs.st-and.ac.uk. n.p. 1996. Web.
Orzel, Chad. “Applications of Quantum Mechanics.” SEEDMAGAZINE.COM. Seed Media Group, 2009. Web.
“Quantum Mechanics.” www2.slac.stanford.edu. SLAC, 2009. Web.