background preloader

Wave function

Wave function
However, complex numbers are not necessarily used in all treatments. Louis de Broglie in his later years proposed a real-valued wave function connected to the complex wave function by a proportionality constant and developed the de Broglie–Bohm theory. The unit of measurement for ψ depends on the system. For one particle in three dimensions, its units are [length]−3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region). Historical background[edit] In the 1920s and 1930s, quantum mechanics was developed using calculus and linear algebra. Wave functions and function spaces[edit] Functional analysis is commonly used to formulate the wave function with a necessary mathematical precision; usually they are quadratically integrable functions (at least locally) because it is compatible with the Hilbert space formalism mentioned below. Requirements[edit]

Understanding Understanding (also called intellection) is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object. Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support intelligent behavior.[1] An understanding is the limit of a conceptualization. To understand something is to have conceptualized it to a given measure. Examples[edit] Understanding as a model[edit] Gregory Chaitin, a noted computer scientist, propounds a view that comprehension is a kind of data compression.[2] In his essay "The Limits of Reason", he argues that understanding something means being able to figure out a simple set of rules that explains it. Components of understanding[edit] Cognition and affect[edit] Religious perspectives[edit] See also[edit]

Quantum tunnelling Quantum mechanical phenomenon In physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, should not be passable due to the object not having sufficient energy to pass or surmount the barrier. Tunneling is a consequence of the wave nature of matter, where the quantum wave function describes the state of a particle or other physical system, and wave equations such as the Schrödinger equation describe their behavior. The probability of transmission of a wave packet through a barrier decreases exponentially with the barrier height, the barrier width, and the tunneling particle's mass, so tunneling is seen most prominently in low-mass particles such as electrons or protons tunneling through microscopically narrow barriers. The effect was predicted in the early 20th century. Introduction to the concept [edit] or where .

Olfaction Volatile small molecule odorants, non-volatile proteins, and non-volatile hydrocarbons may all produce olfactory sensations. Some animal species are able to smell carbon dioxide in minute concentrations.[5] Study of olfaction[edit] Early scientific study of olfaction includes the extensive doctoral dissertation of Eleanor Gamble, published in 1898, which compared olfactory to other stimulus modalities, and implied that smell had a lower intensity discrimination.[6] As the Epicurean and atomistic Roman philosopher Lucretius (1st Century BCE) speculated, different odors are attributed to different shapes and sizes of "atoms" (odor molecules in the modern understanding) that stimulate the olfactory organ [2]. Main olfactory system[edit] In vertebrates smells are sensed by olfactory sensory neurons in the olfactory epithelium. Receptor neuron[edit] Olfactory bulb projections[edit] Accessory olfactory system[edit] Human olfactory system[edit]

Quantum superposition Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular theoretically possible states (or, configuration of its properties) simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics). and . Here is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement. Likewise is the state that will always convert to 1. Concept[edit] The principle of quantum superposition states that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number. For example, if there are two configurations labelled by 0 and 1, the most general state would be .

Somatosensory system Touch is a crucial means of receiving information. This photo shows tactile markings identifying stairs for visually impaired people. While touch (also called tactile perception) is considered one of the five traditional senses, the impression of touch is formed from several modalities including pressure, skin stretch, vibration and temperature. In medicine, the colloquial term "touch" is usually replaced with "somatic senses" to better reflect the variety of mechanisms involved. Somatic senses are sometimes referred to as somesthetic senses, with the understanding that somesthesis includes touch, proprioception and (depending on usage) also haptic perception.[1] Processing primarily occurs in the primary somatosensory area in the parietal lobe of the cerebral cortex: information is sent from the receptors via sensory nerves, through tracts in the spinal cord and finally into the brain. Structure[edit] General somatosensory pathway[edit] Periphery[edit] Spinal cord[edit] Brain[edit]

Quantum nonlocality Quantum nonlocality is the phenomenon by which the measurements made at a microscopic level necessarily refute one or more notions (often referred to as local realism) that are regarded as intuitively true in classical mechanics. Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory. Many entangled quantum states produce such correlations when measured, as demonstrated by Bell's theorem. Experiments have generally favoured quantum mechanics as a description of nature, over local hidden variable theories.[1][2] Any physical theory that supersedes or replaces quantum theory must make similar experimental predictions and must therefore also be nonlocal in this sense; quantum nonlocality is a property of the universe that is independent of our description of nature. Example[edit] Imagine two experimentalists, Alice and Bob, situated in separate laboratories. and P(b0|A1) = or

Taste Taste, gustatory perception, or gustation[1] is the sensory impression of food or other substances on the tongue and is one of the five traditional senses. Taste is the sensation produced when a substance in the mouth reacts chemically with taste receptor cells located on taste buds. Taste, along with smell (olfaction) and trigeminal nerve stimulation (registering texture, pain, and temperature), determines flavors of food or other substances. Humans have taste receptors on taste buds (gustatory calyculi) and other areas including the upper surface of the tongue and the epiglottis.[2][3] The tongue is covered with thousands of small bumps called papillae, which are easily visible to the naked eye. As taste senses both harmful and beneficial things, all basic tastes are classified as either aversive or appetitive, depending upon the effect the things they sense have on our bodies.[10] Sweetness helps to identify energy-rich foods, while bitterness serves as a warning sign of poisons.[11]

Complementarity (physics) In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The complementarity principle was formulated by Niels Bohr, the developer of the Bohr model of the atom, and a leading founder of quantum mechanics.[1] Bohr summarized the principle as follows: ...however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. For example, the particle and wave aspects of physical objects are such complementary phenomena. Physicists F.A.M. Dr.

Hearing (sense) Hearing Hearing, auditory perception, or audition is the ability to perceive sound by detecting vibrations,[1] changes in the pressure of the surrounding medium through time, through an organ such as the ear. Sound may be heard through solid, liquid, or gaseous matter.[2] It is one of the traditional five senses. The inability to hear is called deafness. In humans and other vertebrates, hearing is performed primarily by the auditory system: mechanical waves, known as vibrations are detected by the ear and transduced into nerve impulses that are perceived by the brain (primarily in the temporal lobe). Like touch, audition requires sensitivity to the movement of molecules in the world outside the organism. Hearing mechanism[edit] There are three main components of the human ear: the outer ear, the middle ear, and the inner ear. Outer ear[edit] Middle ear[edit] The middle ear consists of a small air-filled chamber that is located medial to the eardrum. Inner ear[edit] Hearing tests[edit]

Quantum decoherence Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath),[2] since every system is loosely coupled with the energetic state of its surroundings. Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion).[3] Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the system and environment. These have the effect of sharing quantum information with—or transferring it to—the surroundings. Decoherence does not generate actual wave function collapse. It only provides an explanation for the observance of wave function collapse, as the quantum nature of the system "leaks" into the environment. Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Mechanisms[edit] . .

Visual perception Visual perception is the ability to interpret the surrounding environment by processing information that is contained in visible light. The resulting perception is also known as eyesight, sight, or vision (adjectival form: visual, optical, or ocular). The various physiological components involved in vision are referred to collectively as the visual system, and are the focus of much research in psychology, cognitive science, neuroscience, and molecular biology, collectively referred to as vision science. Visual system[edit] Main article: Visual system Note that up until now much of the above paragraph could apply to octopi, mollusks, worms, insects and things more primitive; anything with a more concentrated nervous system and better eyes than say a jellyfish. The perception of objects and the totality of the visual scene is accomplished by the visual association cortex. Study[edit] Early studies[edit] Unconscious inference[edit] Inference requires prior experience of the world. See also[edit]

Related: