Information measures of hydrogenic systems, Laguerre polynomials
... the concept of Shannon’s entropy for more than 20 yr (1925 versus 1948), and (ii) may also be a more intuitive and powerful analytical tool in the approximation theory and quantum physics [7–9]. Here, the Fisher information and the Shannon entropy for arbitrary hydrogenic states are explicitly calcu ...
... the concept of Shannon’s entropy for more than 20 yr (1925 versus 1948), and (ii) may also be a more intuitive and powerful analytical tool in the approximation theory and quantum physics [7–9]. Here, the Fisher information and the Shannon entropy for arbitrary hydrogenic states are explicitly calcu ...
Topological Field Theories in 2 dimensions
... for now let us focus on one important consequence of this structure. Recall that a commutative algebra over C is called semi-simple if it is isomorphic to a direct sum of copies of C. Semi-simple Frobenius algebras are easy to classify: the trace must be diagonal in the basis of projectors, so all w ...
... for now let us focus on one important consequence of this structure. Recall that a commutative algebra over C is called semi-simple if it is isomorphic to a direct sum of copies of C. Semi-simple Frobenius algebras are easy to classify: the trace must be diagonal in the basis of projectors, so all w ...
IO-IY
... 13. Consider the Bohr energy expression (Equation 30.13) as it applies to singly ionized helium He+ (Z = 2) and doubly ionized lithium Li2+ (Z = 3). This expression predicts equal electron energies for these two species for certain values of the quantum number n (the quantum number is different for ...
... 13. Consider the Bohr energy expression (Equation 30.13) as it applies to singly ionized helium He+ (Z = 2) and doubly ionized lithium Li2+ (Z = 3). This expression predicts equal electron energies for these two species for certain values of the quantum number n (the quantum number is different for ...
About John Stachel`s “Structural Realism and Contextual Individuality”
... all, such a predicate as “is one meter from some other point but not from itself” also applies to all points, so does not express a difference between them. Secondly, the deduction, that there are at least two Xs if some X bears an irreflexive relation to some X, does not require the PII! It assumes ...
... all, such a predicate as “is one meter from some other point but not from itself” also applies to all points, so does not express a difference between them. Secondly, the deduction, that there are at least two Xs if some X bears an irreflexive relation to some X, does not require the PII! It assumes ...
Black hole fireworks: quantum-gravity effects outside the horizon
... which corresponds to b = 1. Since this heuristic argument is not very strong, we leave b undetermined below, to show that our point does not strongly depend on it. Note that q may become of order unity for a close enough to 2m and after a sufficiently long elapsed time. In other words: there is no r ...
... which corresponds to b = 1. Since this heuristic argument is not very strong, we leave b undetermined below, to show that our point does not strongly depend on it. Note that q may become of order unity for a close enough to 2m and after a sufficiently long elapsed time. In other words: there is no r ...
Proposing a Classical Explanation of the EPR
... apple), have a fixed number of dimensions as an innate property of its structure. This requires no novel ad hoc hypotheses, since the one entity being proposed (a real spacetime) is observed, and therefore is in evidence. It is also vastly simpler than the other two alternatives. Superstring theory ...
... apple), have a fixed number of dimensions as an innate property of its structure. This requires no novel ad hoc hypotheses, since the one entity being proposed (a real spacetime) is observed, and therefore is in evidence. It is also vastly simpler than the other two alternatives. Superstring theory ...
4 4.1. Particle motion in the presence of a potential barrier
... structures: wells, walls, and barriers. • The calculation of wave functions for barriers and wells involves solution of Schrödinger equation with the application of continuity conditions at boundaries between different values of the potential energy • The results obtained are different from those fo ...
... structures: wells, walls, and barriers. • The calculation of wave functions for barriers and wells involves solution of Schrödinger equation with the application of continuity conditions at boundaries between different values of the potential energy • The results obtained are different from those fo ...
QUANTUM COMPUTING: AN OVERVIEW
... of A: A|λi = λi |λi . Consider a superposition state c1 |λ1 + c2 |λ2 . If we measure a in this state, the state undergoes an abrupt change (wave function collapse) to one of the eigenstates |λi corresponding to the observed eigenvalue λi . Suppose we prepare many copies of the state c1 |λ1 ...
... of A: A|λi = λi |λi . Consider a superposition state c1 |λ1 + c2 |λ2 . If we measure a in this state, the state undergoes an abrupt change (wave function collapse) to one of the eigenstates |λi corresponding to the observed eigenvalue λi . Suppose we prepare many copies of the state c1 |λ1 ...
