Derivation of Spin Projection Operator using Lagrange Interpolation Formula

From reversible computation to quantum computation by Lagrange interpolation

Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w \times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {\bf S}$_{2^w}$. The permutation group P($n$), isomorphic to {\bf S}$_n$, contains cycles with length~$p$, ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By Lagrange interpolation between the $p$~matrices of the cycle, we step from a finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the unitary group U($n$). As U($2^w$) is the group of all possible quantum…

A field-theoretical approach to non-relativistic QED

We give here a field-theoretical derivation of the Hamiltonian of the non-relativistic quantum electrodynamics in the Coulomb gauge using the Lagrange formalism. It leads to the same result as the usual derivation, where one just replaces the classical vector potential in the minimal coupling of the second quantized electron Hamiltonian by the quantized one and adds the photon energy. This approach illustrates however the proper use of the Euler-Lagrange equations and the canonical formalism that fail if one tries to build up the many-body quantum theory starting from the classical theory of p…

类氦离子$(Z,e,e)$的拉格朗日网格方法：对高精度能谱随核电荷数$Z$的插值

Helium-like ions $(Z,e,e)$ in Lagrange Mesh method, interpolating the highly-accurate energy spectra vs. Z

本文提出类氦离子研究的两种方法：基于拉格朗日网格法的高精度数值方法，以及匹配两类展开的少参数插值公式，可对类氦序列任意激发态能谱实现10-14位有效数字的精度，获多项首次结果。