Related papers: Kindergarten Quantum Mechanics
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
This is a collection of lectures given at the University of Heidelberg, especially but not exclusively for people who want to learn something about the canonical approach to quantum gravity, which is however not included in these lectures.…
I review the various algebraic foundations of quantum mechanics. They have been suggested since the birth of this theory till up to last year. They are the following ones: Heisenberg-Born-Jordan (1925), Weyl (1928), Dirac (1930), von…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
Global Categorical Symmetries are a powerful new tool for analyzing quantum field theories. This volume compiles lecture notes from the 2022 and 2023 summer schools on Global Categorical Symmetries, held at the Perimeter Institute for…
Quantum science is in the news daily and engages student interest and curiosity. A fundamental quantum science concept that underpins medical imaging, quantum computing and many future technologies is quantum spin. Quantum spin can explain…
General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-1/2 particles, these…
In this paper we develop a picture of Quantum Mechanics based on the description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest theorems for quantum dynamics. Our basic technical…
Marcella [arXiv:quant-ph/0703126] has presented a straightforward technique employing the Dirac formalism to calculate single- and double-slit interference patterns. He claims that no reference is made to classical optics or scattering…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
In this work, we explore the implications of applying the formalism of symplectic geometry to quantum mechanics, particularly focusing on many-particle systems. We extend the concept of a symplectic indicator of entanglement, originally…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…