# Density matrix

Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. The density operator for this system is[1] By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are[1] For an operator (which describes an observable is given by[1] In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Pure and mixed states In quantum mechanics, a quantum system is represented by a state vector (or ket) . is called a pure state. and a 50% chance that the state vector is . A mixed state is different from a quantum superposition. Example: Light polarization An example of pure and mixed states is light polarization. . and . . .

Second death The second death is an eschatological concept in Judaism and Christianity related to punishment after a first, natural, death. Judaism Although the term is not found in the Hebrew Bible, Sysling in his study (1996) of Teḥiyyat ha-metim (Hebrew; "resurrection of the dead") in the Palestinian Targums identifies a consistent usage of the term "second death" in texts of the Second Temple period and early Rabbinical writings. In most cases this "second death" is identical with the judgment, following resurrection, in Gehinnom at the Last Day.[1] Targum Deuteronomy

Finite potential well The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a box, but one which has finite potential walls. Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling).

No-communication theorem In physics, the no-communication theorem is a no-go theorem from quantum information theory, which states that, during measurement of an entangled quantum state, it is not possible for one observer, making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that suggest the possibility of instantaneous communication. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. Informal Overview The theorem is built on the basic presumption that the laws of quantum mechanics hold.

Matrix mechanics Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. In some contrast to the wave formulation, it produces spectra of energy operators by purely algebraic, ladder operator, methods.[1] Relying on these methods, Pauli derived the hydrogen atom spectrum in 1926,[2] before the development of wave mechanics. Development of matrix mechanics In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Einselection In quantum mechanics, einselection, short for environment - induced superselection, is a name coined by Wojciech H. Zurek[1] for a process which explains the phenomenon of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions. Classicality is an emergent property induced in open quantum systems by their environments. Due to the interaction with the environment, the vast majority of states in the Hilbert space of a quantum open system become highly unstable to entangling interaction with the environment, which in effect monitors selected observables of the system. After a decoherence time, which for macroscopic objects is typically many orders of magnitude shorter than any other dynamical timescale,[2] a generic quantum state decays into an uncertain state which can be decomposed into a mixture of simple pointer states. In this way the environment induces effective superselection rules.

Old Earth creationism Old Earth creationism is an umbrella term for a number of types of creationism, including gap creationism, progressive creationism, and evolutionary creationism.[1] Old Earth creationism is typically more compatible with mainstream scientific thought on the issues of physics, chemistry, geology and the age of the Earth, in comparison to young Earth creationism.[2] Types of old Earth creationism Gap creationism Gap creationism states that life was immediately and recently created on a pre-existing old Earth. Particle in a box In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels.

Quantum teleportation Quantum teleportation is a process by which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for superluminal transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem.

Interpretations of quantum mechanics An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real", and other matters. This question is of special interest to philosophers of physics, as physicists continue to show a strong interest in the subject. They usually consider an interpretation of quantum mechanics as an interpretation of the mathematical formalism of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory.

From Eternity to Book Club: Chapter Eleven | Cosmic Variance Welcome to this week’s installment of the From Eternity to Here book club. Part Three of the book concludes with Chapter Eleven, “Quantum Time.” Excerpt: This distinction between “incomplete knowledge” and “intrinsic quantum indeterminacy” is worth dwelling on. If the wave function tells us there is a 75 percent chance of observing the cat under the table and a 25 percent chance of observing her on the sofa, that does not mean there is a 75 percent chance that the cat is under the table and a 25 percent chance that she is on the sofa. There is no such thing as “where the cat is.” Young Earth creationism Young Earth Creationism (YEC) is the religious belief[1] that the Universe, Earth and all life on Earth were created by direct acts of the Abrahamic God during a relatively short period, between 5,700 and 10,000 years ago.[2] Its primary adherents are those Christians and Jews[3] who, using a literal interpretation of the Genesis creation narrative as a basis, believe that God created the Earth in six 24-hour days.[4][5] Young Earth Creationists differ from other creationists in that they believe in a strict-literal interpretation of the Bible regarding the age of the Earth. This contrasts with Old Earth Creationists, who believe that the Book of Genesis may be interpreted metaphorically and who accept the scientifically determined age of Earth and the universe.[6] Since the mid-20th century, young Earth Creationists starting with Henry M.

Solution of Schrödinger equation for a step potential In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension. Typically, the potential is modelled as a Heaviside step function. Calculation Schrödinger equation and potential function Scattering at a finite potential step of height V0, shown in green.

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