The mathematics of quantum mechanics
eBook - ePub

The mathematics of quantum mechanics

Alessio Mangoni

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eBook - ePub

The mathematics of quantum mechanics

Alessio Mangoni

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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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Information

Year
2020
ISBN
9788835885627

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:
ļæ¼
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
ļæ¼
image-118.png
on the state ket
ļæ¼
image-119.png
such that
ļæ¼
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,
ļæ¼
image-121.png
and
ļæ¼
image-122.png
Two operators
ļæ¼
image-123.png
are equal if their action on an arbitrary ket is the same, i.e.
ļæ¼
image-124.png

Null operator

In particular an...

Table of contents