Canonical Transformations in Quantum Mechanics
... The quantum canonical transformations provide a unified approach to the integrability of quantum systems. One may define as quantum integrable (“in the sense of canonical transformations”) those problems whose general solution can be constructed as a finite product of elementary canonical transforma ...
... The quantum canonical transformations provide a unified approach to the integrability of quantum systems. One may define as quantum integrable (“in the sense of canonical transformations”) those problems whose general solution can be constructed as a finite product of elementary canonical transforma ...
Three Myths About Time Reversal in Quantum Theory 1. Introduction
... category. But before we get that far: why do we expect time reversal to preserve inner products between rays? Or, in terms of the underlying Hilbert space vectors, why should time reversal preserve transition probabilities? Of course, Wigner is free to define words however he likes. But one would li ...
... category. But before we get that far: why do we expect time reversal to preserve inner products between rays? Or, in terms of the underlying Hilbert space vectors, why should time reversal preserve transition probabilities? Of course, Wigner is free to define words however he likes. But one would li ...
Heisenberg Spin Chains : from Quantum Groups to
... eigenstate basis and obtain their matrix elements to be summed up to perform the trace, and the scalar products, necessary in the actual computation of (4) or (5). The solution to these different steps turns out to be a fantastic challenge involving deep algebraic structures hidden in the original B ...
... eigenstate basis and obtain their matrix elements to be summed up to perform the trace, and the scalar products, necessary in the actual computation of (4) or (5). The solution to these different steps turns out to be a fantastic challenge involving deep algebraic structures hidden in the original B ...
Observing a coherent superposition of an atom and a
... has led to the proposed superselection rules for some quantities and not others. While this gedanken experiment served to illustrate a concept, recent advances in the preparation and manipulation of exotic quantum states of matter may offer the opportunity to demonstrate these concepts in experiment ...
... has led to the proposed superselection rules for some quantities and not others. While this gedanken experiment served to illustrate a concept, recent advances in the preparation and manipulation of exotic quantum states of matter may offer the opportunity to demonstrate these concepts in experiment ...
Quantum Mechanics for Pedestrians 1: Fundamentals
... Before attending the quantum mechanics course, the students have had among others an introduction to atomic physics: relevant phenomena, experiments and simple calculations should therefore be familiar to them. Nevertheless, experience has shown that at the start of the lectures, some students do no ...
... Before attending the quantum mechanics course, the students have had among others an introduction to atomic physics: relevant phenomena, experiments and simple calculations should therefore be familiar to them. Nevertheless, experience has shown that at the start of the lectures, some students do no ...
Through scattering theory with gun and camera: Coping with conventions
... T-matrix elements must contain 共in the second term兲 both the delta function ␦共Ek⬘ − Ek兲 and the on-shell restriction. Forgetting this implication can lead to incorrect equations and procedures, such as simply writing Eq. 共31兲 in momentum space as ␦共k⬘ − k兲 − 2i具k⬘兩T̂兩k典. This expression, versions o ...
... T-matrix elements must contain 共in the second term兲 both the delta function ␦共Ek⬘ − Ek兲 and the on-shell restriction. Forgetting this implication can lead to incorrect equations and procedures, such as simply writing Eq. 共31兲 in momentum space as ␦共k⬘ − k兲 − 2i具k⬘兩T̂兩k典. This expression, versions o ...
here
... Why is this a p-wave superconductor? For the so-called s-, p-, d- or f-wave superconductor ...
... Why is this a p-wave superconductor? For the so-called s-, p-, d- or f-wave superconductor ...
A Noncommutative Sigma Model by Mauritz van den Worm
... and study some of its more interesting properties, such as the fact that it can be written as a crossed product which will greatly aid us in determining its K-theory and the unique trace on the quantum torus. The final section of Chapter 1 deals with a finite dimensional representation of the quantu ...
... and study some of its more interesting properties, such as the fact that it can be written as a crossed product which will greatly aid us in determining its K-theory and the unique trace on the quantum torus. The final section of Chapter 1 deals with a finite dimensional representation of the quantu ...
Spin Algebra, Spin Eigenvalues, Pauli Matrices Lecture 10
... But suppose you keep hitting s, m with S+ . The eigenvalue of S2 will not change, but the eigenvalue of Sz keeps increasing. If we keep doing this enough, the eigenvalue of Sz will grow larger than the square root of the eigenvalue of S2 . That is, the z-component of the angular momentum vector wil ...
... But suppose you keep hitting s, m with S+ . The eigenvalue of S2 will not change, but the eigenvalue of Sz keeps increasing. If we keep doing this enough, the eigenvalue of Sz will grow larger than the square root of the eigenvalue of S2 . That is, the z-component of the angular momentum vector wil ...
Iterants, Fermions and the Dirac Equation
... associated with the group G onto the ring of n × n matrices. As a result we see that iterant algebra is fundamental to all matrix algebra. Section 4 ends with a number of classical examples including iterant represtations for quaternion algebra. Section 5 goes back to n × n matrices and shows how th ...
... associated with the group G onto the ring of n × n matrices. As a result we see that iterant algebra is fundamental to all matrix algebra. Section 4 ends with a number of classical examples including iterant represtations for quaternion algebra. Section 5 goes back to n × n matrices and shows how th ...
Symmetry breaking - Corso di Fisica Nucleare
... 3-momentum (p = 0) and non-zero energy11 (p0 6= 0). If the previous relation is valid then12 hn|Ja0 (x)|0i = 0 x = (x, t) is also valid (because of the way we have chosen the momentum), which is the same as hn|∂µ Jaµ (x)|0i = 0 . ...
... 3-momentum (p = 0) and non-zero energy11 (p0 6= 0). If the previous relation is valid then12 hn|Ja0 (x)|0i = 0 x = (x, t) is also valid (because of the way we have chosen the momentum), which is the same as hn|∂µ Jaµ (x)|0i = 0 . ...
draft
... Finally, an operator concave function f is a function such that −f is operator convex. In all three cases it is assumed that the inequalities hold for all matrix sizes (so that an operator monotone function is always monotone in the ordinary sense, but the converse may fail). 1 The definitions are s ...
... Finally, an operator concave function f is a function such that −f is operator convex. In all three cases it is assumed that the inequalities hold for all matrix sizes (so that an operator monotone function is always monotone in the ordinary sense, but the converse may fail). 1 The definitions are s ...
diatomic molecular spectroscopy with standard and anomalous
... as Klein's [2] anomalous commutation formula. Two approaches are debated in this work, namely an operator and an algebraic approach, without utilizing Klein's anomalous commutation formula. Each approach begins with the standard commutator formula, Eq. (3). We point out that in principle, Eq. (4) ca ...
... as Klein's [2] anomalous commutation formula. Two approaches are debated in this work, namely an operator and an algebraic approach, without utilizing Klein's anomalous commutation formula. Each approach begins with the standard commutator formula, Eq. (3). We point out that in principle, Eq. (4) ca ...
Charge and spin quantum fluids generated by many
... is the study of such a relation. Our study is motivated by both the unusual finite-energy spectral properties observed in quasi-1D materials [3,4] and the relation of these materials to two-dimensional (2D) quantum problems [5–7]. In a chemical potential µ and magnetic field h the 1D Hubbard Hamilto ...
... is the study of such a relation. Our study is motivated by both the unusual finite-energy spectral properties observed in quasi-1D materials [3,4] and the relation of these materials to two-dimensional (2D) quantum problems [5–7]. In a chemical potential µ and magnetic field h the 1D Hubbard Hamilto ...
Regularity and Approximability of Electronic Wave Functions
... where the sum extends over the multi-indices k = (k1 , . . . , kd ) ∈ Nd and its convergence has to be understood in the L2 -sense. The speed of convergence of this series depends on that with which the expansion coefficients ub(k) decay. Assume, for example, that u is continuously differentiable, w ...
... where the sum extends over the multi-indices k = (k1 , . . . , kd ) ∈ Nd and its convergence has to be understood in the L2 -sense. The speed of convergence of this series depends on that with which the expansion coefficients ub(k) decay. Assume, for example, that u is continuously differentiable, w ...