elements of quantum mechanics
... photon concept and the wave theory of light complement each other. Thus, all forms of electromagnetic radiation can be described from two points of view. In one extreme electromagnetic waves describe interference and diffraction pattern formed by a large number of photons while in other extreme, the ...
... photon concept and the wave theory of light complement each other. Thus, all forms of electromagnetic radiation can be described from two points of view. In one extreme electromagnetic waves describe interference and diffraction pattern formed by a large number of photons while in other extreme, the ...
Trajectory-Wave Approach to Electron Dynamics in Hydrogen Atom
... occur along a trajectory the presence of which is a reflection of the existence of a particle, as well as it is assumed that any motion is defined by a wave V(x,t). It is assumed that there is an explicit relationship between the trajectory and wave equations of the electron, which are established o ...
... occur along a trajectory the presence of which is a reflection of the existence of a particle, as well as it is assumed that any motion is defined by a wave V(x,t). It is assumed that there is an explicit relationship between the trajectory and wave equations of the electron, which are established o ...
3D simulation of a silicon quantum dot in
... We have developed a code for the simulation of silicon quantum dots with current spin density functional theory, that allows us to simulate the electrical and spin properties of dots with up to 50 electrons in the presence of magnetic field. Silicon quantum dots exhibit a very rich spin behavior, du ...
... We have developed a code for the simulation of silicon quantum dots with current spin density functional theory, that allows us to simulate the electrical and spin properties of dots with up to 50 electrons in the presence of magnetic field. Silicon quantum dots exhibit a very rich spin behavior, du ...
Quantum statistics: Is there an effective fermion repulsion or boson
... The quantity inside the curly brackets is the partition function for two quantum particles. The first term is the classical partition function, and its contribution already is accounted for in the classical ideal gas pressure; it cancels out in Eq. 共13兲. The second term corrects the incorrect classi ...
... The quantity inside the curly brackets is the partition function for two quantum particles. The first term is the classical partition function, and its contribution already is accounted for in the classical ideal gas pressure; it cancels out in Eq. 共13兲. The second term corrects the incorrect classi ...
Lecture notes lecture 13 (quantum physics)
... energy is a whole number of quantas. The correct mathematical work to Planck’s work was later done by Erwin Schroedinger, an Austrian scientist. ...
... energy is a whole number of quantas. The correct mathematical work to Planck’s work was later done by Erwin Schroedinger, an Austrian scientist. ...
chapter40
... Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties The de Broglie wavelength of a particle is ...
... Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties The de Broglie wavelength of a particle is ...
Quantum diffusion of electromagnetic fields of ultrarelativistic spin
... It has been known for a while that very intense electromagnetic fields are created in ultrarelativistic hadronic and nuclear collisions [1–5]. However, no convincing experimental evidence of their impact on the scattering dynamics has been observed. In recent years, a renewed interest to this subjec ...
... It has been known for a while that very intense electromagnetic fields are created in ultrarelativistic hadronic and nuclear collisions [1–5]. However, no convincing experimental evidence of their impact on the scattering dynamics has been observed. In recent years, a renewed interest to this subjec ...
a new insight into the quantization of energy
... that thermal energy is bundled into tiny quantum units.5 Albert Einstein used Planck’s constant and showed that the energy of light is bundled into particle like photons.6 The principle of quantum correspondence emerged with the appearance of the photon. It states that the square of the amplitude of ...
... that thermal energy is bundled into tiny quantum units.5 Albert Einstein used Planck’s constant and showed that the energy of light is bundled into particle like photons.6 The principle of quantum correspondence emerged with the appearance of the photon. It states that the square of the amplitude of ...
1 Classical mechanics vs. quantum mechanics - Assets
... The state function can also be expressed alternatively as a function of another canonic variable ‘‘conjugate’’ to the position coordinate of the system, the linear momentum of the particle px, or C(px, t). The basic problem of the dynamics of the particle can be formulated in either equivalent form, ...
... The state function can also be expressed alternatively as a function of another canonic variable ‘‘conjugate’’ to the position coordinate of the system, the linear momentum of the particle px, or C(px, t). The basic problem of the dynamics of the particle can be formulated in either equivalent form, ...
fundamental_reality\holographic paradigm\morphogenetic fields
... understand what quantum mechanics means by such a model you get quite a strong analogy to a formative field. Sheldrake: Yes, it may even be a homology; it may be a different way of talking about the same thing. Bohm: The major difference is that quantum mechanics doesn't treat time, and therefore i ...
... understand what quantum mechanics means by such a model you get quite a strong analogy to a formative field. Sheldrake: Yes, it may even be a homology; it may be a different way of talking about the same thing. Bohm: The major difference is that quantum mechanics doesn't treat time, and therefore i ...
1 Classical mechanics vs. quantum mechanics - Beck-Shop
... The state function can also be expressed alternatively as a function of another canonic variable ‘‘conjugate’’ to the position coordinate of the system, the linear momentum of the particle px, or C(px, t). The basic problem of the dynamics of the particle can be formulated in either equivalent form, ...
... The state function can also be expressed alternatively as a function of another canonic variable ‘‘conjugate’’ to the position coordinate of the system, the linear momentum of the particle px, or C(px, t). The basic problem of the dynamics of the particle can be formulated in either equivalent form, ...
1 Classical Mechanics
... i.e. the time integral of the Lagrangian between fixed endpoints. Fixed endpoints means that the initial (qk (t1 )) and final (qk (t2 )) values of the coordinates held fixed. To visualize what this means, think of a pitcher in baseball, throwing a baseball intended to hit a specific location in the stri ...
... i.e. the time integral of the Lagrangian between fixed endpoints. Fixed endpoints means that the initial (qk (t1 )) and final (qk (t2 )) values of the coordinates held fixed. To visualize what this means, think of a pitcher in baseball, throwing a baseball intended to hit a specific location in the stri ...
Wave function
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).For a given system, once a representation corresponding to a maximal set of commuting observables and a suitable coordinate system is chosen, the wave function is a complex-valued function of the system's degrees of freedom corresponding to the chosen representation and coordinate system, continuous as well as discrete. Such a set of observables, by a postulate of quantum mechanics, are Hermitian linear operators on the space of states representing a set of physical observables, like position, momentum and spin that can, in principle, be simultaneously measured with arbitrary precision. Wave functions can be added together and multiplied by complex numbers to form new wave functions, and hence are elements of a vector space. This is the superposition principle of quantum mechanics. This vector space is endowed with an inner product such that it is a complete metric topological space with respect to the metric induced by the inner product. In this way the set of wave functions for a system form a function space that is a Hilbert space. The inner product is a measure of the overlap between physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The actual space depends on the system's degrees of freedom (hence on the chosen representation and coordinate system) and the exact form of the Hamiltonian entering the equation governing the dynamical behavior. In the non-relativistic case, disregarding spin, this is the Schrödinger equation.The Schrödinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name ""wave function"", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical ""space"", and in this respect it differs fundamentally from water waves or waves on a string.For a given system, the choice of which relevant degrees of freedom to use are not unique, and correspondingly the domain of the wave function is not unique. It may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. These descriptions are the most important, but they are not the only possibilities. Just like in classical mechanics, canonical transformations may be used in the description of a quantum system. Some particles, like electrons and photons, have nonzero spin, and the wave function must include this fundamental property as an intrinsic discrete degree of freedom. In general, for a particle with half-integer spin the wave function is a spinor, for a particle with integer spin the wave function is a tensor. Particles with spin zero are called scalar particles, those with spin 1 vector particles, and more generally for higher integer spin, tensor particles. The terminology derives from how the wave functions transform under a rotation of the coordinate system. No elementary particle with spin 3⁄2 or higher is known, except for the hypothesized spin 2 graviton. Other discrete variables can be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).In the Copenhagen interpretation, an interpretation of quantum mechanics, the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place at a given time or having a definite momentum, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.The unit of measurement for ψ depends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.