Comprehensive analysis of electron correlations in
... do doubly excited states of a many-electron atom resemble those of a two-electron atom? In what way is the description to be modified for doubly excited states of a many-electron atom? Second, can one make the next step to understand the correlation of triply excited states? Both questions can be ad ...
... do doubly excited states of a many-electron atom resemble those of a two-electron atom? In what way is the description to be modified for doubly excited states of a many-electron atom? Second, can one make the next step to understand the correlation of triply excited states? Both questions can be ad ...
Symmetry In The Dissociative Recombination Of Polyatomic Ions
... eect in order to model the non Born-Oppenheimer vibronic coupling in linear polyatomic ions. The coupling has shown to represent the main mechanism responsible for electronic capturing in highly excited Rydberg states associated with excited vibrational levels of the ionic core. We consider all int ...
... eect in order to model the non Born-Oppenheimer vibronic coupling in linear polyatomic ions. The coupling has shown to represent the main mechanism responsible for electronic capturing in highly excited Rydberg states associated with excited vibrational levels of the ionic core. We consider all int ...
the fermi liquid as a renormalization group fixed point
... developments in this rapidly advancing field see, for example, Refs. [16,17] and more references therein.] Current interest in the physics of strongly correlated fermions [non-Fermi Liquids in d > 1] inspired a new wave of efforts aimed at clarifying the foundations of the Landau FLT and possible me ...
... developments in this rapidly advancing field see, for example, Refs. [16,17] and more references therein.] Current interest in the physics of strongly correlated fermions [non-Fermi Liquids in d > 1] inspired a new wave of efforts aimed at clarifying the foundations of the Landau FLT and possible me ...
Optical properties of cylindrical nanowires
... For oblique incidence the direction of propagation of the incident wave makes an angle θ with the normal to the z -axis, see Figure 1.1. Furthermore the cylinder is assumed to be surrounded by vacuum and the refractive index of the cylinder is equal to m. In case of a surrounding homogeneous medium ...
... For oblique incidence the direction of propagation of the incident wave makes an angle θ with the normal to the z -axis, see Figure 1.1. Furthermore the cylinder is assumed to be surrounded by vacuum and the refractive index of the cylinder is equal to m. In case of a surrounding homogeneous medium ...
Quantum-Secure Message Authentication Codes
... Quantum secure MACs. In the classical settings many MAC systems are based on the observation that a secure pseudorandom function gives rise to a secure MAC [BKR00, BCK96]. We begin by studying the same question in the quantum settings. Very recently Zhandry [Zha12b] defined the concept of a quantum ...
... Quantum secure MACs. In the classical settings many MAC systems are based on the observation that a secure pseudorandom function gives rise to a secure MAC [BKR00, BCK96]. We begin by studying the same question in the quantum settings. Very recently Zhandry [Zha12b] defined the concept of a quantum ...
Revised B. Sc. Honours in Physics (under CBCS) w.e.f. 2015-2018
... A candidate has to answer Five Questions out of Nine Questions of which Question no. 1 is compulsory and will be of short answer type to be answered in about 100 words (4 Questions to be answered out of 8). Out of the remaining 08 (eight) Questions, 04 (four) are to be answered. Each question carrie ...
... A candidate has to answer Five Questions out of Nine Questions of which Question no. 1 is compulsory and will be of short answer type to be answered in about 100 words (4 Questions to be answered out of 8). Out of the remaining 08 (eight) Questions, 04 (four) are to be answered. Each question carrie ...
Lecture I: Collective Excitations: From Particles to Fields Free Scalar
... We have seen how the elementary excitations of the quantum chain can be presented in terms of new elementary quasi-particles by the ladder operator formalism. Can this approach be generalised to accommodate other many-body systems? The answer is provided by the method of second quantisation — an ess ...
... We have seen how the elementary excitations of the quantum chain can be presented in terms of new elementary quasi-particles by the ladder operator formalism. Can this approach be generalised to accommodate other many-body systems? The answer is provided by the method of second quantisation — an ess ...
Destructive quantum interference in spin tunneling problems
... The problem of calculating the rate at which a quantum spin system tunnels between its different low-energy states has been of interest in various different contexts [1]. The tunneling amplitude is usually calculated by setting up a coherent-spin-state path integral and analytically continuing to i ...
... The problem of calculating the rate at which a quantum spin system tunnels between its different low-energy states has been of interest in various different contexts [1]. The tunneling amplitude is usually calculated by setting up a coherent-spin-state path integral and analytically continuing to i ...
Charge and spin quantum fluids generated by many
... is the cν rapidity-momentum functional and the function Θν,ν (x) is defined in Eq. (B.5) of Appendix B. Eqs. (13)–(15) apply to all regular energy eigenstates. The ground state and the low-energy eigenstates involve occupancy configurations of the c and s1 pseudoparticle branches only [19]. The ps ...
... is the cν rapidity-momentum functional and the function Θν,ν (x) is defined in Eq. (B.5) of Appendix B. Eqs. (13)–(15) apply to all regular energy eigenstates. The ground state and the low-energy eigenstates involve occupancy configurations of the c and s1 pseudoparticle branches only [19]. The ps ...
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.