English grammar

Present continuous (I am doing) Usage: in the middle of ‘action’, started doing and haven’t finished yet; talk about things/changes happening in a period around now (for example, today / this week / this evening etc.). Often the action is happening at the time of speaking, but not necessarily. Standard structure: Subject Present tense of be Present participle verb I am (’m) / am not (’m not, ain’t) -ing form of verb he/she/it/name of a person is (’s) / is not (’s not, isn’t) -ing form of verb we/you/they/name of group are (’re) / are not (’re not,aren’t) -ing form of verb For framing a question, reverse the first 2 columns. »

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Theory of groups for physics applications

Week 1 Introduction The origins of Group theory is in Premutations (the algebra obeyed) and Geometry (rotations) corresponding to Discrete and Continuous groups respectively. Geometric rotations, in general do not commute. Continuous groups is essentially Trignomentry. In quantum mechanics, symmetry group substitutes for the geometry of shape and size. Algebraic preliminaries Sets and maps Mathematicians usually classify maps as: Surjective/onto: Range is completely covered. Injective/into: One to One, but need not exhaust range. »

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Notes for GRE Math Review

Arithematic r = c - qd, r is the reminder and q is the quotient when an integer c is divided by a positive integer d The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. 1 is not a prime number. 2 is the only prime number that is even. The fraction part’s value of a mixed number has to be between 0 and 1. »

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Notes for the course PH5211

Nuclear Physics Stable nuclei, Nomenclature and units Atomic scale is 10-10m, nuclear scale is 10-15m. For convenience we use the unit Fermi (fm) = 10-15m = 1 femtometer. Nuclear sizes range from 1 fm to 7 fm. Particle physics usually happens at an even smaller scale << 10-15m. A nuclear species or nuclide is denoted by \(^A_ZX_N\). Here, X is the chemical symbol. Z is the atomic number: the number of protons. »

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Solution manual for Quantum Computation and Quantum Information

Table of Contents 1 Introduction and Overview 2 Introduction to quantum mechanics 1 Introduction and Overview Exercise 1 Exercise 2 Problem 1 Problem 2 Exercise 1 It is already shown that a deterministic classical computer would require \(2^n/2+1\) queries. Instead, if we use a probabilistic classical computer i.e, \(f(x)\) is evaluated for randomly chosen \(x\), with just one execution we cannot determine whether \(f(x)\) is constant or balanced function (atleast not with probability of error ε < 1⁄2). »

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