The mathematics of quantum mechanics

Alessio Mangoni

• Éditeur: Alessio Mangoni
• Année: 2020
• ISBN:
  9788835885627
• Sujet: Physical Sciences
• Sous-sujet: Quantum Theory

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.

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:



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



on the state ket



such that



Action on ket and bra

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



and



Two operators



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



Null operator

In particular an...