The mathematics of quantum mechanics
eBook - ePub

The mathematics of quantum mechanics

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

The mathematics of quantum mechanics

About this book

In this book we expose the mathematics for quantum mechanics. The main topics are: vectors, ket and bra space, properties and operations, product for a scalar, internal product between ket and bra, norm and Schwarz inequality, orthogonality, operators and their operations, operator acting on kets as a measure of an observable for a physical state, adjoint operator, hermitian operators, unitary operator, external product, projectors, basis of eigenkets, representation of vectors and operators, matrix algebra.

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Yes, you can access The mathematics of quantum mechanics by Alessio Mangoni in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Quantum Theory. We have over one million books available in our catalogue for you to explore.

Information

Operators

Observables are physical quantities that can be measured. Mathematically we associate an operator to each observable.
An X operator is indicated by the symbol:

image-117.png
Measuring the physical quantity x for the physical state a means to apply, from the left, the operator associated with it, that is

image-118.png
on the state ket

image-119.png
such that

image-120.png

Action on ket and bra

An operator always acts to the left of a ket or to the right of a bra,

image-121.png
and

image-122.png
Two operators

image-123.png
are equal if their action on an arbitrary ket is the same, i.e.

image-124.png

Null operator

In particular an...

Table of contents

  1. Index
  2. Introduction
  3. Ket space
  4. Bra space
  5. Internal product
  6. Operators
  7. Representation of vectors and operators