On some log-cosine integrals related to (3), (4), and (6)
... the evaluation of matrix elements of powers of the logarithm function. In the classical case, these integrals would be of interest when the position distribution function of the motion is written in terms of trigonometric functions. In the quantum case, trigonometric wavefunctions lead to similar in ...
... the evaluation of matrix elements of powers of the logarithm function. In the classical case, these integrals would be of interest when the position distribution function of the motion is written in terms of trigonometric functions. In the quantum case, trigonometric wavefunctions lead to similar in ...
Schroedinger`s Model of Hydrogen Atom
... The hydrogen atom is the simplest atom. It has only one electron and the nucleus is a proton. It is therefore not surprising that it has been the test-bed for new theories. In this module, we will look at the attempts that have been made to understand the structure of the hydrogen atom1—1a structure ...
... The hydrogen atom is the simplest atom. It has only one electron and the nucleus is a proton. It is therefore not surprising that it has been the test-bed for new theories. In this module, we will look at the attempts that have been made to understand the structure of the hydrogen atom1—1a structure ...
The Status of our Ordinary Three Dimensions in a Quantum Universe 1
... promising. According to this version of quantum mechanics, formulated perhaps best by John von Neumann in 1932, states of quantum systems evolve according to two fundamental laws, the Schrödinger equation and what we will call ‘the collapse postulate’.6 Both laws describe the evolution of quantum s ...
... promising. According to this version of quantum mechanics, formulated perhaps best by John von Neumann in 1932, states of quantum systems evolve according to two fundamental laws, the Schrödinger equation and what we will call ‘the collapse postulate’.6 Both laws describe the evolution of quantum s ...
Modern Factoring Algorithms
... locations containing 1. The r0 s corresponding to these locations are the ones we are interested in. Its still not very clear as to how the modified f would make the sieving procedure faster compared to the previous function (because the above procedure could have been applied in the simple algorith ...
... locations containing 1. The r0 s corresponding to these locations are the ones we are interested in. Its still not very clear as to how the modified f would make the sieving procedure faster compared to the previous function (because the above procedure could have been applied in the simple algorith ...
Light interference from single atoms and their mirror images
... light. But the characteristics of this light depend strongly on the environment of the atom1,2. For example, if an atom is placed between two mirrors, both the total rate and the spectral composition of the spontaneous emission can be modi®ed. Such effects have been observed using various systems: m ...
... light. But the characteristics of this light depend strongly on the environment of the atom1,2. For example, if an atom is placed between two mirrors, both the total rate and the spectral composition of the spontaneous emission can be modi®ed. Such effects have been observed using various systems: m ...
- Philsci
... brains in vats. In fact, in some ways the wave function ontology is even more radical than the brain in the vat scenario: in the brain in the vat scenario, at least we are correct in thinking that we have brains existing in a three-dimensional space. According to the wave function ontology, even th ...
... brains in vats. In fact, in some ways the wave function ontology is even more radical than the brain in the vat scenario: in the brain in the vat scenario, at least we are correct in thinking that we have brains existing in a three-dimensional space. According to the wave function ontology, even th ...
“Anticoherent” Spin States via the Majorana Representation
... as nearly as possible to a classical spin vector pointing in a given direction n̂. Coherent spin states are a conceptual attractor for physicists in part because they mimic classical spin angular momentum as much as possible. As useful as this makes the coherent states, in theory and in practice, it ...
... as nearly as possible to a classical spin vector pointing in a given direction n̂. Coherent spin states are a conceptual attractor for physicists in part because they mimic classical spin angular momentum as much as possible. As useful as this makes the coherent states, in theory and in practice, it ...
Quantum Phenomena in Condensed Phase
... the quantum system density matrix that incorporates ideas from both methods yet maintains the ease of implementation of linearized methods. The method is based on a time stepping procedure arising from a Trotter factorization, combining the forward and backward incremental propagators, and treating ...
... the quantum system density matrix that incorporates ideas from both methods yet maintains the ease of implementation of linearized methods. The method is based on a time stepping procedure arising from a Trotter factorization, combining the forward and backward incremental propagators, and treating ...
ABSTRACT PHOTON PAIR PRODUCTION FROM A HOT ATOMIC ENSEMBLE IN THE DIAMOND CONFIGURATION
... 1.1 Introduction: The Basics of the System This thesis is concerned with the experimental demonstration of a quantum mechanically correlated photon pair source. The generation medium used here is a laser pumped vapor cell of warm rubidium. The scheme takes advantage of a spontaneous four wave-mixing ...
... 1.1 Introduction: The Basics of the System This thesis is concerned with the experimental demonstration of a quantum mechanically correlated photon pair source. The generation medium used here is a laser pumped vapor cell of warm rubidium. The scheme takes advantage of a spontaneous four wave-mixing ...
Quantum methods for clock synchronization: Beating the standard
... The second traditional method for clock synchronization is known as the Eddington slow clock transport. In this protocol, Alice synchronizes a “wristwatch” (a clock that can easily be transported) with her own clock, and then adiabatically [37] transports the wristwatch to Bob. Bob can then determin ...
... The second traditional method for clock synchronization is known as the Eddington slow clock transport. In this protocol, Alice synchronizes a “wristwatch” (a clock that can easily be transported) with her own clock, and then adiabatically [37] transports the wristwatch to Bob. Bob can then determin ...
Entanglement and its Role in Shor`s Algorithm
... measurement. We also note (from calculating the entanglement of formation for appropriate pairs of qubits) that there is no pairwise entanglement between any pair of qubits at any of the sampled points in this instance of the algorithm. Jozsa and Linden [4] showed that this and similar gate models f ...
... measurement. We also note (from calculating the entanglement of formation for appropriate pairs of qubits) that there is no pairwise entanglement between any pair of qubits at any of the sampled points in this instance of the algorithm. Jozsa and Linden [4] showed that this and similar gate models f ...
IAP-VI-02-Annex_I-Section_I
... Today a major trend in fundamental sciences is the study of nonlinear systems and the appearance of complex behavior. Such systems are characterized by many interacting entities as in macroscopic physics where systems composed of many microscopic particles present collective and nonlinear phenomena ...
... Today a major trend in fundamental sciences is the study of nonlinear systems and the appearance of complex behavior. Such systems are characterized by many interacting entities as in macroscopic physics where systems composed of many microscopic particles present collective and nonlinear phenomena ...
Full text in PDF form
... Since in what follows we proceed only from the existence of fundamental length, it should be noted that this fact was established apart from GUR as well. For instance, from an ideal experiment associated with Gravitational Field and Quantum Mechanics a lower bound on minimal length was obtained in [ ...
... Since in what follows we proceed only from the existence of fundamental length, it should be noted that this fact was established apart from GUR as well. For instance, from an ideal experiment associated with Gravitational Field and Quantum Mechanics a lower bound on minimal length was obtained in [ ...
Aggregation Operations from Quantum Computing
... of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary qTs. This paper introduces an interpretation of aggregations obtained by classical fuzzy states, that is, by multi-dimensional quantum register associated to mFs on unitary interval U . In particular, t-norms ...
... of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary qTs. This paper introduces an interpretation of aggregations obtained by classical fuzzy states, that is, by multi-dimensional quantum register associated to mFs on unitary interval U . In particular, t-norms ...
Manifestly Covariant Functional Measures for Quantum Field Theory
... where † denotes Hermitian conjugate. Although we are dealing with real fields, it is convenient to allow the modes to enter in complex conjugate pairs. In this case det M is real and so we may include complex conjugation in equation (35). Alternatively, we could just use a transpose and instead of ...
... where † denotes Hermitian conjugate. Although we are dealing with real fields, it is convenient to allow the modes to enter in complex conjugate pairs. In this case det M is real and so we may include complex conjugation in equation (35). Alternatively, we could just use a transpose and instead of ...
Transformations of Entangled Mixed States of Two Qubits
... fundamental unit is called a quantum bit (with the abbreviation qubit)[31]. A qubit not only takes the values of either 0 or 1, but also it can take on values which are superpositions of both 0 and 1. In other words, both values are possible for one qubit due to the superposition principle in quantu ...
... fundamental unit is called a quantum bit (with the abbreviation qubit)[31]. A qubit not only takes the values of either 0 or 1, but also it can take on values which are superpositions of both 0 and 1. In other words, both values are possible for one qubit due to the superposition principle in quantu ...
Quantum violation of classical physics in macroscopic systems
... macroscopic everyday world. While microscopic particles, such as photons, electrons or even large molecules, can nowadays be put into superposition or entangled states [17–19], the concept that a macroscopic object, such as a cat, could be in a superposition state, seems, in Schrödinger’s words, bur ...
... macroscopic everyday world. While microscopic particles, such as photons, electrons or even large molecules, can nowadays be put into superposition or entangled states [17–19], the concept that a macroscopic object, such as a cat, could be in a superposition state, seems, in Schrödinger’s words, bur ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.