Misplaced Pages

#4995

62-506: Venus Optics was founded in 2013. Founder, managing director and chief developer is Dayong Li who graduated in opto-electronic engineering from the Beijing Institute of Technology . The company develops and produces innovative photographic lenses under the brand name Laowa ('old frog'). Laowa's optics designer, Dayong Li, is believed to be the optics designer of Tamron , the reputable camera lens manufacturer from Japan. He

124-480: A {\displaystyle a} larger we make the spread in momentum smaller, but the spread in position gets larger. This illustrates the uncertainty principle. As we let the Gaussian wave packet evolve in time, we see that its center moves through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that

186-466: A definite prediction of what the quantum state ψ ( t ) {\displaystyle \psi (t)} will be at any later time. Some wave functions produce probability distributions that are independent of time, such as eigenstates of the Hamiltonian . Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example,

248-510: A family of unitary operators parameterized by a variable t {\displaystyle t} . Under the evolution generated by A {\displaystyle A} , any observable B {\displaystyle B} that commutes with A {\displaystyle A} will be conserved. Moreover, if B {\displaystyle B} is conserved by evolution under A {\displaystyle A} , then A {\displaystyle A}

310-471: A loss of information, though: knowing the reduced density matrices of the individual systems is not enough to reconstruct the state of the composite system. Just as density matrices specify the state of a subsystem of a larger system, analogously, positive operator-valued measures (POVMs) describe the effect on a subsystem of a measurement performed on a larger system. POVMs are extensively used in quantum information theory. As described above, entanglement

372-426: A mathematical formulation of quantum mechanics and survey its application to some useful and oft-studied examples. In the mathematically rigorous formulation of quantum mechanics, the state of a quantum mechanical system is a vector ψ {\displaystyle \psi } belonging to a ( separable ) complex Hilbert space H {\displaystyle {\mathcal {H}}} . This vector

434-417: A measurement of its position and also at the same time for a measurement of its momentum . Another consequence of the mathematical rules of quantum mechanics is the phenomenon of quantum interference , which is often illustrated with the double-slit experiment . In the basic version of this experiment, a coherent light source , such as a laser beam, illuminates a plate pierced by two parallel slits, and

496-471: A probability amplitude. Applying the Born rule to these amplitudes gives a probability density function for the position that the electron will be found to have when an experiment is performed to measure it. This is the best the theory can do; it cannot say for certain where the electron will be found. The Schrödinger equation relates the collection of probability amplitudes that pertain to one moment of time to

558-405: A single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus , whereas in quantum mechanics, it is described by a static wave function surrounding the nucleus. For example, the electron wave function for an unexcited hydrogen atom is a spherically symmetric function known as an s orbital ( Fig. 1 ). Analytic solutions of

620-551: A single spatial dimension. A free particle is one which is not subject to external influences, so that its Hamiltonian consists only of its kinetic energy: The general solution of the Schrödinger equation is given by which is a superposition of all possible plane waves e i ( k x − ℏ k 2 2 m t ) {\displaystyle e^{i(kx-{\frac {\hbar k^{2}}{2m}}t)}} , which are eigenstates of

682-473: Is and this provides the lower bound on the product of standard deviations: Another consequence of the canonical commutation relation is that the position and momentum operators are Fourier transforms of each other, so that a description of an object according to its momentum is the Fourier transform of its description according to its position. The fact that dependence in momentum is the Fourier transform of

SECTION 10

#1732800786005

744-469: Is a fundamental theory that describes the behavior of nature at and below the scale of atoms . It is the foundation of all quantum physics , which includes quantum chemistry , quantum field theory , quantum technology , and quantum information science . Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary ( macroscopic and (optical) microscopic ) scale, but

806-478: Is a key feature of models of measurement processes in which an apparatus becomes entangled with the system being measured. Systems interacting with the environment in which they reside generally become entangled with that environment, a phenomenon known as quantum decoherence . This can explain why, in practice, quantum effects are difficult to observe in systems larger than microscopic. There are many mathematically equivalent formulations of quantum mechanics. One of

868-424: Is a valid joint state that is not separable. States that are not separable are called entangled . If the state for a composite system is entangled, it is impossible to describe either component system A or system B by a state vector. One can instead define reduced density matrices that describe the statistics that can be obtained by making measurements on either component system alone. This necessarily causes

930-405: Is conserved under the evolution generated by B {\displaystyle B} . This implies a quantum version of the result proven by Emmy Noether in classical ( Lagrangian ) mechanics: for every differentiable symmetry of a Hamiltonian, there exists a corresponding conservation law . The simplest example of a quantum system with a position degree of freedom is a free particle in

992-1066: Is considered as a sum over all possible classical and non-classical paths between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics. The Hamiltonian H {\displaystyle H} is known as the generator of time evolution, since it defines a unitary time-evolution operator U ( t ) = e − i H t / ℏ {\displaystyle U(t)=e^{-iHt/\hbar }} for each value of t {\displaystyle t} . From this relation between U ( t ) {\displaystyle U(t)} and H {\displaystyle H} , it follows that any observable A {\displaystyle A} that commutes with H {\displaystyle H} will be conserved : its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator A {\displaystyle A} can generate

1054-446: Is e.g., the 100 mm f/2,8 2x Ultra Macro APO) are purely manual lenses. There is no communication between the camera body and the lens, hence, no transfer of Exif data, no autofocus function, no lens-based image stabilization (OIS), and no automatic aperture control . However, autofocus plays a minor role in macro and wide angle photography. Auto focus bracketing is not possible with manual lenses. The company does not exclude

1116-448: Is given by The operator U ( t ) = e − i H t / ℏ {\displaystyle U(t)=e^{-iHt/\hbar }} is known as the time-evolution operator, and has the crucial property that it is unitary . This time evolution is deterministic in the sense that – given an initial quantum state ψ ( 0 ) {\displaystyle \psi (0)} – it makes

1178-406: Is its associated eigenvector. More generally, the eigenvalue is degenerate and the probability is given by ⟨ ψ , P λ ψ ⟩ {\displaystyle \langle \psi ,P_{\lambda }\psi \rangle } , where P λ {\displaystyle P_{\lambda }} is the projector onto its associated eigenspace. In

1240-726: Is known as wave–particle duality . In addition to light, electrons , atoms , and molecules are all found to exhibit the same dual behavior when fired towards a double slit. Another non-classical phenomenon predicted by quantum mechanics is quantum tunnelling : a particle that goes up against a potential barrier can cross it, even if its kinetic energy is smaller than the maximum of the potential. In classical mechanics this particle would be trapped. Quantum tunnelling has several important consequences, enabling radioactive decay , nuclear fusion in stars, and applications such as scanning tunnelling microscopy , tunnel diode and tunnel field-effect transistor . When quantum systems interact,

1302-444: Is not possible for the solution to be a single momentum eigenstate, or a single position eigenstate, as these are not normalizable quantum states. Instead, we can consider a Gaussian wave packet : which has Fourier transform, and therefore momentum distribution We see that as we make a {\displaystyle a} smaller the spread in position gets smaller, but the spread in momentum gets larger. Conversely, by making

SECTION 20

#1732800786005

1364-628: Is not sufficient for describing them at very small submicroscopic (atomic and subatomic ) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation, valid at large (macroscopic/microscopic) scale. Quantum systems have bound states that are quantized to discrete values of energy , momentum , angular momentum , and other quantities, in contrast to classical systems where these quantities can be measured continuously. Measurements of quantum systems show characteristics of both particles and waves ( wave–particle duality ), and there are limits to how accurately

1426-479: Is often erroneously used as a synonym, but is a wider branch of physics that concerns all interactions between light and electric fields , whether or not they form part of an electronic device. Optoelectronics is based on the quantum mechanical effects of light on electronic materials, especially semiconductors , sometimes in the presence of electric fields . Important applications of optoelectronics include: Quantum mechanics Quantum mechanics

1488-815: Is part of quantum communication protocols, such as quantum key distribution and superdense coding . Contrary to popular misconception, entanglement does not allow sending signals faster than light , as demonstrated by the no-communication theorem . Another possibility opened by entanglement is testing for " hidden variables ", hypothetical properties more fundamental than the quantities addressed in quantum theory itself, knowledge of which would allow more exact predictions than quantum theory provides. A collection of results, most significantly Bell's theorem , have demonstrated that broad classes of such hidden-variable theories are in fact incompatible with quantum physics. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then

1550-540: Is postulated to be normalized under the Hilbert space inner product, that is, it obeys ⟨ ψ , ψ ⟩ = 1 {\displaystyle \langle \psi ,\psi \rangle =1} , and it is well-defined up to a complex number of modulus 1 (the global phase), that is, ψ {\displaystyle \psi } and e i α ψ {\displaystyle e^{i\alpha }\psi } represent

1612-466: Is replaced by − i ℏ ∂ ∂ x {\displaystyle -i\hbar {\frac {\partial }{\partial x}}} , and in particular in the non-relativistic Schrödinger equation in position space the momentum-squared term is replaced with a Laplacian times − ℏ 2 {\displaystyle -\hbar ^{2}} . When two different quantum systems are considered together,

1674-415: Is the reduced Planck constant . The constant i ℏ {\displaystyle i\hbar } is introduced so that the Hamiltonian is reduced to the classical Hamiltonian in cases where the quantum system can be approximated by a classical system; the ability to make such an approximation in certain limits is called the correspondence principle . The solution of this differential equation

1736-469: Is then If the state for the first system is the vector ψ A {\displaystyle \psi _{A}} and the state for the second system is ψ B {\displaystyle \psi _{B}} , then the state of the composite system is Not all states in the joint Hilbert space H A B {\displaystyle {\mathcal {H}}_{AB}} can be written in this form, however, because

1798-410: The 5th Laowa Photo Competition and sponsored prize for the event. Laowa Video Marathon is an invitation-only program launched by Laowa in 2021. It has gathered 10 videographers and YouTubers, including Motoaki(Aki from Japan), Jason Morris, Helena Gudkova(cameragirlhelena), Yeyoph and more. The program consists of 10 one-minute long short films. Each video's beginning would match the ending shot from

1860-505: The Born rule : in the simplest case the eigenvalue λ {\displaystyle \lambda } is non-degenerate and the probability is given by | ⟨ λ → , ψ ⟩ | 2 {\displaystyle |\langle {\vec {\lambda }},\psi \rangle |^{2}} , where λ → {\displaystyle {\vec {\lambda }}}

1922-713: The canonical commutation relation : Given a quantum state, the Born rule lets us compute expectation values for both X {\displaystyle X} and P {\displaystyle P} , and moreover for powers of them. Defining the uncertainty for an observable by a standard deviation , we have and likewise for the momentum: The uncertainty principle states that Either standard deviation can in principle be made arbitrarily small, but not both simultaneously. This inequality generalizes to arbitrary pairs of self-adjoint operators A {\displaystyle A} and B {\displaystyle B} . The commutator of these two operators

Venus Optics - Misplaced Pages Continue

1984-423: The photoelectric effect . These early attempts to understand microscopic phenomena, now known as the " old quantum theory ", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr , Erwin Schrödinger , Werner Heisenberg , Max Born , Paul Dirac and others. The modern theory is formulated in various specially developed mathematical formalisms . In one of them, a mathematical entity called

2046-562: The wave function provides information, in the form of probability amplitudes , about what measurements of a particle's energy, momentum, and other physical properties may yield. Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles. It has been demonstrated to hold for complex molecules with thousands of atoms, but its application to human beings raises philosophical problems, such as Wigner's friend , and its application to

2108-431: The Hilbert space for the spin of a single proton is simply the space of two-dimensional complex vectors C 2 {\displaystyle \mathbb {C} ^{2}} with the usual inner product. Physical quantities of interest – position, momentum, energy, spin – are represented by observables, which are Hermitian (more precisely, self-adjoint ) linear operators acting on

2170-411: The Hilbert space of the combined system is the tensor product of the Hilbert spaces of the two components. For example, let A and B be two quantum systems, with Hilbert spaces H A {\displaystyle {\mathcal {H}}_{A}} and H B {\displaystyle {\mathcal {H}}_{B}} , respectively. The Hilbert space of the composite system

2232-432: The Hilbert space. A quantum state can be an eigenvector of an observable, in which case it is called an eigenstate , and the associated eigenvalue corresponds to the value of the observable in that eigenstate. More generally, a quantum state will be a linear combination of the eigenstates, known as a quantum superposition . When an observable is measured, the result will be one of its eigenvalues with probability given by

2294-489: The Schrödinger equation are known for very few relatively simple model Hamiltonians including the quantum harmonic oscillator , the particle in a box , the dihydrogen cation , and the hydrogen atom . Even the helium atom – which contains just two electrons – has defied all attempts at a fully analytic treatment, admitting no solution in closed form . However, there are techniques for finding approximate solutions. One method, called perturbation theory , uses

2356-403: The analytic result for a simple quantum mechanical model to create a result for a related but more complicated model by (for example) the addition of a weak potential energy . Another approximation method applies to systems for which quantum mechanics produces only small deviations from classical behavior. These deviations can then be computed based on the classical motion. One consequence of

2418-506: The background details (e.g., where and how the subject lives) in the photo. Due to physical reasons, the working distance in the macro range is rather short (at 1:1, focusing distance is 12.2 cm resulting in a working distance of only 4.7 mm). In the meantime, Venus Optics have released unique lenses mainly in the fields of ultra macro and rectilinear and/or fast ultra wide angle lenses for full frame, APS-C , MFT , and Fujifilm G-Mount (see table). Most Laowa lenses (an exception

2480-606: The basic quantum formalism is the uncertainty principle. In its most familiar form, this states that no preparation of a quantum particle can imply simultaneously precise predictions both for a measurement of its position and for a measurement of its momentum. Both position and momentum are observables, meaning that they are represented by Hermitian operators . The position operator X ^ {\displaystyle {\hat {X}}} and momentum operator P ^ {\displaystyle {\hat {P}}} do not commute, but rather satisfy

2542-404: The collection of probability amplitudes that pertain to another. One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between measurable quantities. The most famous form of this uncertainty principle says that no matter how a quantum particle is prepared or how carefully experiments upon it are arranged, it is impossible to have a precise prediction for

Venus Optics - Misplaced Pages Continue

2604-626: The continuous case, these formulas give instead the probability density . After the measurement, if result λ {\displaystyle \lambda } was obtained, the quantum state is postulated to collapse to λ → {\displaystyle {\vec {\lambda }}} , in the non-degenerate case, or to P λ ψ / ⟨ ψ , P λ ψ ⟩ {\textstyle P_{\lambda }\psi {\big /}\!{\sqrt {\langle \psi ,P_{\lambda }\psi \rangle }}} , in

2666-431: The dependence in position means that the momentum operator is equivalent (up to an i / ℏ {\displaystyle i/\hbar } factor) to taking the derivative according to the position, since in Fourier analysis differentiation corresponds to multiplication in the dual space . This is why in quantum equations in position space, the momentum p i {\displaystyle p_{i}}

2728-510: The development of more lenses with electronics in them. Since 2017, Laowa had organised multiple international marketing campaigns bearing its slogan "New Idea, New Fun" . Laowa has used competition as an advertising vehicle to encourage its users to share their image. The company first started organising Laowa Photo Competition in 2017. Initially focusing on photos from its own lenses, and later it also allow images taken with other brand's lenses. As of 2021, there are other brands collaborate in

2790-415: The general case. The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr–Einstein debates , in which the two scientists attempted to clarify these fundamental principles by way of thought experiments . In the decades after the formulation of quantum mechanics,

2852-462: The interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave). However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. This behavior

2914-733: The last video. In early 2021, Laowa interviewed multiple up-and-coming photographers and introduced them as " Laowagrapher ". It consists group of photographers from all over the world. Optoelectronics Optoelectronics (or optronics ) is the study and application of electronic devices and systems that find, detect and control light , usually considered a sub-field of photonics . In this context, light often includes invisible forms of radiation such as gamma rays , X-rays , ultraviolet and infrared , in addition to visible light. Optoelectronic devices are electrical-to-optical or optical-to-electrical transducers , or instruments that use such devices in their operation. Electro-optics

2976-430: The light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere , producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles rather than waves;

3038-432: The momentum operator with momentum p = ℏ k {\displaystyle p=\hbar k} . The coefficients of the superposition are ψ ^ ( k , 0 ) {\displaystyle {\hat {\psi }}(k,0)} , which is the Fourier transform of the initial quantum state ψ ( x , 0 ) {\displaystyle \psi (x,0)} . It

3100-413: The oldest and most common is the " transformation theory " proposed by Paul Dirac , which unifies and generalizes the two earliest formulations of quantum mechanics – matrix mechanics (invented by Werner Heisenberg ) and wave mechanics (invented by Erwin Schrödinger ). An alternative formulation of quantum mechanics is Feynman 's path integral formulation , in which a quantum-mechanical amplitude

3162-412: The one-dimensional case in the x {\displaystyle x} direction, the time-independent Schrödinger equation may be written With the differential operator defined by with state ψ {\displaystyle \psi } in this case having energy E {\displaystyle E} coincident with the kinetic energy of the particle. The general solutions of

SECTION 50

#1732800786005

3224-455: The original quantum system ceases to exist as an independent entity (see Measurement in quantum mechanics ). The time evolution of a quantum state is described by the Schrödinger equation: Here H {\displaystyle H} denotes the Hamiltonian , the observable corresponding to the total energy of the system, and ℏ {\displaystyle \hbar }

3286-428: The position becomes more and more uncertain. The uncertainty in momentum, however, stays constant. The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and therefore infinite potential energy everywhere outside that region. For

3348-400: The question of what constitutes a "measurement" has been extensively studied. Newer interpretations of quantum mechanics have been formulated that do away with the concept of " wave function collapse " (see, for example, the many-worlds interpretation ). The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wave functions become entangled so that

3410-413: The result can be the creation of quantum entanglement : their properties become so intertwined that a description of the whole solely in terms of the individual parts is no longer possible. Erwin Schrödinger called entanglement "... the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought". Quantum entanglement enables quantum computing and

3472-566: The results of a Bell test will be constrained in a particular, quantifiable way. Many Bell tests have been performed and they have shown results incompatible with the constraints imposed by local hidden variables. It is not possible to present these concepts in more than a superficial way without introducing the mathematics involved; understanding quantum mechanics requires not only manipulating complex numbers, but also linear algebra , differential equations , group theory , and other more advanced subjects. Accordingly, this article will present

3534-463: The same physical system. In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space . The exact nature of this Hilbert space is dependent on the system – for example, for describing position and momentum the Hilbert space is the space of complex square-integrable functions L 2 ( C ) {\displaystyle L^{2}(\mathbb {C} )} , while

3596-625: The superposition principle implies that linear combinations of these "separable" or "product states" are also valid. For example, if ψ A {\displaystyle \psi _{A}} and ϕ A {\displaystyle \phi _{A}} are both possible states for system A {\displaystyle A} , and likewise ψ B {\displaystyle \psi _{B}} and ϕ B {\displaystyle \phi _{B}} are both possible states for system B {\displaystyle B} , then

3658-441: The theory is that it usually cannot predict with certainty what will happen, but only give probabilities. Mathematically, a probability is found by taking the square of the absolute value of a complex number , known as a probability amplitude. This is known as the Born rule , named after physicist Max Born . For example, a quantum particle like an electron can be described by a wave function, which associates to each point in space

3720-437: The universe as a whole remains speculative. Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy . For example, the refinement of quantum mechanics for the interaction of light and matter, known as quantum electrodynamics (QED), has been shown to agree with experiment to within 1 part in 10 when predicting the magnetic properties of an electron. A fundamental feature of

3782-526: The value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle ). Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck 's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein 's 1905 paper , which explained

SECTION 60

#1732800786005

3844-472: Was heavily involved in numerous Tamron 's project development including the popular 24-70mm f/2.8 and 70-200mm f/2.8. The first lens was the 60 mm f/2.8 2 x Ultra Macro, a full frame lens with a magnification factor of 2:1 that could also be focused to infinity which is unique. In the same year, Venus Optics released the widest angle macro lens to offer a 1:1 magnification ratio, the 15 mm f/4 Wide Angle Macro. The small focal length allows to include

#4995