Energy levelA quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules.
Quantum mechanicsQuantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
Hydrogen atomA hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe. In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary (diatomic) hydrogen gas, H2.
Introduction to quantum mechanicsQuantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain.
Degenerate energy levelsIn quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy (or simply the degeneracy) of the level.
Hydrogen-like atomA hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen. Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such as Rb and Cs, singly ionized alkaline earth metals such as Ca+ and Sr+ and other ions such as He+, Li2+, and Be3+ and isotopes of any of the above. A hydrogen-like atom includes a positively charged core consisting of the atomic nucleus and any core electrons as well as a single valence electron.
Quantum stateIn quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system. Quantum states may be defined in different ways for different kinds of systems or problems.
Interpretations of quantum mechanicsAn interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
Energy conservationEnergy conservation is the effort to reduce wasteful energy consumption by using fewer energy services. This can be done by using energy more effectively (using less energy for continuous service) or changing one's behavior to use less service (for example, by driving less). Energy conservation can be achieved through efficient energy use, which has some advantages, including a reduction in greenhouse gas emissions and a smaller carbon footprint, as well as cost, water, and energy savings.
Levelized cost of electricityThe levelized cost of electricity (LCOE) is a measure of the average net present cost of electricity generation for a generator over its lifetime. It is used for investment planning and to compare different methods of electricity generation on a consistent basis. The more general term levelized cost of energy may include the costs of either electricity or heat. The latter is also referred to as levelized cost of heat or levelized cost of heating (LCOH), or levelized cost of thermal energy.
Energy subsidyEnergy subsidies are measures that keep prices for customers below market levels, or for suppliers above market levels, or reduce costs for customers and suppliers. Energy subsidies may be direct cash transfers to suppliers, customers, or related bodies, as well as indirect support mechanisms, such as tax exemptions and rebates, price controls, trade restrictions, and limits on market access. The International Renewable Energy Agency tracked some $634 billion in energy-sector subsidies in 2020, and found that around 70% were fossil fuel subsidies.
Efficient energy useEfficient energy use, sometimes simply called energy efficiency, is the process of reducing the amount of energy required to provide products and services. For example, insulating a building allows it to use less heating and cooling energy to achieve and maintain a thermal comfort. Installing light-emitting diode bulbs, fluorescent lighting, or natural skylight windows reduces the amount of energy required to attain the same level of illumination compared to using traditional incandescent light bulbs.
Relational quantum mechanicsRelational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.
History of quantum mechanicsThe history of quantum mechanics is a fundamental part of the history of modern physics. The major chapters of this history begin with the emergence of quantum ideas to explain individual phenomena -- blackbody radiation, the photoelectric effect, solar emission spectra -- an era called the Old or Older quantum theories. The invention of wave mechanics by Schrodinger and expanded by many others triggers the "modern" era beginning around 1925.
Measurement in quantum mechanicsIn quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.
Quantum harmonic oscillatorThe quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.
OmOm (or Aum) (; ॐ, ओम्) is a symbol representing a sacred sound, syllable, mantra, and an invocation in Hinduism. Its written representation is one of the most important symbols of Hinduism. It is variously said to be the essence of the supreme Absolute, consciousness, Ātman, Brahman, or the cosmic world. In Indic traditions, Om serves as a sonic representation of the divine, a standard of Vedic authority and a central aspect of soteriological doctrines and practices.
HydrogenHydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, and highly combustible. Hydrogen is the most abundant chemical substance in the universe, constituting roughly 75% of all normal matter. Stars such as the Sun are mainly composed of hydrogen in the plasma state. Most of the hydrogen on Earth exists in molecular forms such as water and organic compounds.
Om mani padme hum(ॐ मणि पद्मे हूँ, õːː mɐɳɪ pɐdmeː ɦũː) is the six-syllabled Sanskrit mantra particularly associated with the four-armed Shadakshari form of Avalokiteshvara, the bodhisattva of compassion. It first appeared in the Mahayana Kāraṇḍavyūhasūtra where it is also referred to as the sadaksara (six syllabled) and the paramahrdaya, or “innermost heart” of Avalokiteshvara. In this text the mantra is seen as the condensed form of all Buddhist teachings. The precise meaning and significance of the words remains much discussed by Buddhist scholars.
