Negative probability
... ‘discontinuous’ loses part of its sense, which leads us into stepping beyond logic, maybe to the “language” of being: Let us divide an infinite set, e.g. that of integers, into two compact subsets, so that any element of the initial set belongs to just one of the two subsets. The method of diagonali ...
... ‘discontinuous’ loses part of its sense, which leads us into stepping beyond logic, maybe to the “language” of being: Let us divide an infinite set, e.g. that of integers, into two compact subsets, so that any element of the initial set belongs to just one of the two subsets. The method of diagonali ...
Anyons and the quantum Hall effect— A pedagogical
... satisfy Schroedinger’s wave equation. And second, these wave functions should satisfy certain symmetry properties with respect to the exchange of identical particles. For fermions the wave function should be anti-symmetric, for bosons it should be symmetric. It is impossible to overrate the importan ...
... satisfy Schroedinger’s wave equation. And second, these wave functions should satisfy certain symmetry properties with respect to the exchange of identical particles. For fermions the wave function should be anti-symmetric, for bosons it should be symmetric. It is impossible to overrate the importan ...
Quantum theory without measurement or state reduction problems
... Macroscopic systems are not, under ordinary circumstances, isolated. They cannot be isolated if we can see them. They interact with their own radiation field and that of other objects. They absorb cosmic background radiation photons. Due to their extremely dense energy spectra, they are coupled with ...
... Macroscopic systems are not, under ordinary circumstances, isolated. They cannot be isolated if we can see them. They interact with their own radiation field and that of other objects. They absorb cosmic background radiation photons. Due to their extremely dense energy spectra, they are coupled with ...
Slides - Agenda
... An exact procedure for computing many-particle Bohmian trajectories The correlations are introduced into the time-dependent potentials 4th The interacting potential from (a classical-like) Bohmian trajectories 5th There is a real potential to account for “non-classical” correlations 6th There is a i ...
... An exact procedure for computing many-particle Bohmian trajectories The correlations are introduced into the time-dependent potentials 4th The interacting potential from (a classical-like) Bohmian trajectories 5th There is a real potential to account for “non-classical” correlations 6th There is a i ...
Lecture Notes in Quantum Mechanics Doron Cohen
... [4] A. Messiah, Quantum Mechanics. [for the graduates] The major attempt in this set of lectures was to give a self contained presentation of quantum mechanics, which is not based on the historical ”quantization” approach. The main inspiration comes from Ref.[3] and Ref.[1]. The challenge was to fin ...
... [4] A. Messiah, Quantum Mechanics. [for the graduates] The major attempt in this set of lectures was to give a self contained presentation of quantum mechanics, which is not based on the historical ”quantization” approach. The main inspiration comes from Ref.[3] and Ref.[1]. The challenge was to fin ...
Chapter 10.
... 10.1. Introduction. Classes of Oracles for Grover Algorithm It is well-known that a quantum algorithm can be orders of magnitude more efficient than a standard algorithm. Unfortunately, there are very few algorithms in addition to the famous Shor [Shor94] and Grover [Grover96] algorithms that are kn ...
... 10.1. Introduction. Classes of Oracles for Grover Algorithm It is well-known that a quantum algorithm can be orders of magnitude more efficient than a standard algorithm. Unfortunately, there are very few algorithms in addition to the famous Shor [Shor94] and Grover [Grover96] algorithms that are kn ...
Evolving Quantum circuits - Portland State University
... distinguishable different states of a qudit. These states can be a photon’s polarizations or an elementary particle’s spins. After encoding these distinguishable quantities into multiple-valued constants, a notation for ternary qudit states is |0>, |1> and |2> (we discuss only ternary quantum logic ...
... distinguishable different states of a qudit. These states can be a photon’s polarizations or an elementary particle’s spins. After encoding these distinguishable quantities into multiple-valued constants, a notation for ternary qudit states is |0>, |1> and |2> (we discuss only ternary quantum logic ...
Operator Quantum Error Correction.
... part of this scheme opens up the possibility of studying noiseless subsystems for arbitrary quantum operations. This paper is an expanded and more detailed version of the work [1]. We provide complete details for proofs sketched there, and in some cases we present an alternative “operator” approach ...
... part of this scheme opens up the possibility of studying noiseless subsystems for arbitrary quantum operations. This paper is an expanded and more detailed version of the work [1]. We provide complete details for proofs sketched there, and in some cases we present an alternative “operator” approach ...
III. Contact-ing Schrödinger
... experimentally observed energy levels of the hydrogen atom, scientists applied it to increasingly more complicated atoms and by 1960 had achieved good agreement with experimentally measured results for all atoms in the periodic table (Herman and Skillman (1963)). It should be noted, however, that th ...
... experimentally observed energy levels of the hydrogen atom, scientists applied it to increasingly more complicated atoms and by 1960 had achieved good agreement with experimentally measured results for all atoms in the periodic table (Herman and Skillman (1963)). It should be noted, however, that th ...
Wellposedness of a nonlinear, logarithmic Schrödinger equation of
... effects. This potential has been used, for example, to study wave packet tunnelling through barriers. On the other hand, meaningful physical interpretations have been also given to the presence of the logarithmic potential log(n) in the Schrödinger equation. Indeed, it can be understood as the effe ...
... effects. This potential has been used, for example, to study wave packet tunnelling through barriers. On the other hand, meaningful physical interpretations have been also given to the presence of the logarithmic potential log(n) in the Schrödinger equation. Indeed, it can be understood as the effe ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.