Mathematical Aspects of Quantum Theory and Quantization Summer
... of their scientific interest, think of Atiyah, Manin, Connes. My lectures here will try to give a local, modest, very modest, microscopic push in the other direction. What topics will be discussed in these lectures? The general subject is quantum theory, as a physical theory, but with an emphasis on ...
... of their scientific interest, think of Atiyah, Manin, Connes. My lectures here will try to give a local, modest, very modest, microscopic push in the other direction. What topics will be discussed in these lectures? The general subject is quantum theory, as a physical theory, but with an emphasis on ...
Observations on Hyperplane: II. Dynamical Variables and
... question is yes. But I asked my questioner if he agreed that his question was analogous to asking, within non-relativistic quantum theory, another question. That question is whether an observable at a given time could always be expressed as a function of observables at the time, t = 0, and whether, ...
... question is yes. But I asked my questioner if he agreed that his question was analogous to asking, within non-relativistic quantum theory, another question. That question is whether an observable at a given time could always be expressed as a function of observables at the time, t = 0, and whether, ...
Complete Analytical Solutions of the Mie
... N-dimensional Schrödinger equation have been severally solved by some researchers with the special transformation of the N -dimensional Schrödinger equation. For instance, Bateman et al. investigated the relationship between the hydrogen atom and a harmonic oscillator potential in arbitrary dimensio ...
... N-dimensional Schrödinger equation have been severally solved by some researchers with the special transformation of the N -dimensional Schrödinger equation. For instance, Bateman et al. investigated the relationship between the hydrogen atom and a harmonic oscillator potential in arbitrary dimensio ...
acta physica slovaca vol. 50 No. 1, 1 – 198 February 2000
... (linear) quantum mechanics (QM), providing a general framework of several physical theories. It contains QM itself, its (almost all up to now published) nonlinear modifications and extensions, and also its “semiclassical approximations”, together with the Hamiltonian classical mechanics (CM). This i ...
... (linear) quantum mechanics (QM), providing a general framework of several physical theories. It contains QM itself, its (almost all up to now published) nonlinear modifications and extensions, and also its “semiclassical approximations”, together with the Hamiltonian classical mechanics (CM). This i ...
Quantum Error Correction - Quantum Theory Group at CMU
... while there are many possible choices for bases, even orthonormal bases. The choice of basis is a matter of convenience. • Similarly, a quantum code is best thought of not just as a collection of codewords, as in classical codes, but as a subspace P of the Hilbert space Hc of the code carriers, a su ...
... while there are many possible choices for bases, even orthonormal bases. The choice of basis is a matter of convenience. • Similarly, a quantum code is best thought of not just as a collection of codewords, as in classical codes, but as a subspace P of the Hilbert space Hc of the code carriers, a su ...
Mixed-quantum-state detection with inconclusive results
... operators i of the form i ⫽ 兩 i 典具 i 兩 for a set of linearly dependent vectors 兩 i 典 , then there is no measurement that will result in P E ⫽0. Nonetheless, we may seek the measurement operators that minimize P E , or equivalently, maximize P D , subject to P I ⫽  for some  ⬍1. By allowi ...
... operators i of the form i ⫽ 兩 i 典具 i 兩 for a set of linearly dependent vectors 兩 i 典 , then there is no measurement that will result in P E ⫽0. Nonetheless, we may seek the measurement operators that minimize P E , or equivalently, maximize P D , subject to P I ⫽  for some  ⬍1. By allowi ...
Mutually Unbiased bases: a brief survey
... for all i, j, r 6= s. This leads to our first and most important definition: Definition 1.3. Let B1 = {|ϕ1 i , ..., |ϕd i} and B2 = {|φ1 i , ..., |φd i} be orthonormal bases in the d-dimensional state space. Then they are said to be mutually unbiased if and only if | hϕi |φj i | = √1d for all i, j. ...
... for all i, j, r 6= s. This leads to our first and most important definition: Definition 1.3. Let B1 = {|ϕ1 i , ..., |ϕd i} and B2 = {|φ1 i , ..., |φd i} be orthonormal bases in the d-dimensional state space. Then they are said to be mutually unbiased if and only if | hϕi |φj i | = √1d for all i, j. ...
A Matrix Realignment Method for Recognizing Entanglement
... systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the Peres-Horodecki criterion [i.e., PPT (positive partial transposition) criterion], ...
... systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the Peres-Horodecki criterion [i.e., PPT (positive partial transposition) criterion], ...
Regularity and Approximability of Electronic Wave Functions
... Of at least equal importance in the given context are the regularity properties of the eigenfunctions, whose study began with [49]. For newer developments in this direction, see [32] and [45]. Surveys on the mathematical theory of Schrödinger operators and the quantum N-body problem in particular a ...
... Of at least equal importance in the given context are the regularity properties of the eigenfunctions, whose study began with [49]. For newer developments in this direction, see [32] and [45]. Surveys on the mathematical theory of Schrödinger operators and the quantum N-body problem in particular a ...
![arXiv:1312.4758v2 [quant-ph] 10 Apr 2014](http://s1.studyres.com/store/data/021352507_1-d587dd4045ccae4ae6a47bb17173f358-300x300.png)
arXiv:1312.4758v2 [quant-ph] 10 Apr 2014
... Both QM A(k) and the complexity classes in the current paper are larger than QM A but, apart from that, they do not seem to be related. The complexity of spectral gap has also been studied in the context when the number of qubits grows to infinity (and the Hamiltonian is translationally invariant an ...
... Both QM A(k) and the complexity classes in the current paper are larger than QM A but, apart from that, they do not seem to be related. The complexity of spectral gap has also been studied in the context when the number of qubits grows to infinity (and the Hamiltonian is translationally invariant an ...
6 Product Operators
... The Hamiltonian, H, is the special name given to the operator for the energy of the system. This operator is exceptionally important as its eigenvalues and eigenfunctions are the "energy levels" of the system, and it is transitions between these energy levels which are detected in spectroscopy. To u ...
... The Hamiltonian, H, is the special name given to the operator for the energy of the system. This operator is exceptionally important as its eigenvalues and eigenfunctions are the "energy levels" of the system, and it is transitions between these energy levels which are detected in spectroscopy. To u ...