Physlib.QuantumMechanics.FiniteTarget.HilbertSpace

The Hilbert space of a finite target quantum mechanical system

6 declarations

definition

$n$ -dimensional complex Hilbert space $\mathbb{C}^n$

For a given natural number $n$ , the definition `FiniteHilbertSpace n` represents the $n$ -dimensional complex Hilbert space, mathematically equivalent to $\mathbb{C}^n$ , constructed as the Euclidean space over the complex numbers $\mathbb{C}$ with coordinates indexed by the finite set $\{0, 1, \dots, n-1\}$ .

instance

Additive commutative group structure of $\mathbb{C}^n$

#instAddCommGroupFiniteHilbertSpace

For any natural number $n$ , the $n$ -dimensional complex Hilbert space $\mathbb{C}^n$ (represented by `FiniteHilbertSpace n`) is equipped with the structure of an additive commutative group.

instance

Complex vector space structure of $\mathbb{C}^n$

#instModuleComplexFiniteHilbertSpace

For any natural number $n$ , the $n$ -dimensional complex Hilbert space $\mathbb{C}^n$ (represented by `FiniteHilbertSpace n`) is equipped with the structure of a vector space over the field of complex numbers $\mathbb{C}$ .

instance

Normed additive commutative group structure of $\mathbb{C}^n$

#instNormedAddCommGroupFiniteHilbertSpace

For any natural number $n$ , the $n$ -dimensional complex Hilbert space $\mathbb{C}^n$ (represented by `FiniteHilbertSpace n`) is equipped with the structure of a normed additive commutative group.

instance

Inner product space structure of $\mathbb{C}^n$ over $\mathbb{C}$

#instInnerProductSpaceComplexFiniteHilbertSpace

For any natural number $n$ , the $n$ -dimensional complex Hilbert space $\mathbb{C}^n$ (represented by `FiniteHilbertSpace n`) is equipped with the structure of an inner product space over the field of complex numbers $\mathbb{C}$ .

instance

$\mathbb{C}^n$ is a complete space

#instCompleteSpaceFiniteHilbertSpace

For any natural number $n$ , the $n$ -dimensional complex Hilbert space $\mathbb{C}^n$ is a complete space.

Physlib.QuantumMechanics.FiniteTarget.HilbertSpace

The Hilbert space of a finite target quantum mechanical system

nnn-dimensional complex Hilbert space Cn\mathbb{C}^nCn

Additive commutative group structure of Cn\mathbb{C}^nCn

Complex vector space structure of Cn\mathbb{C}^nCn

Normed additive commutative group structure of Cn\mathbb{C}^nCn

Inner product space structure of Cn\mathbb{C}^nCn over C\mathbb{C}C

Cn\mathbb{C}^nCn is a complete space

$n$ -dimensional complex Hilbert space $\mathbb{C}^n$

Additive commutative group structure of $\mathbb{C}^n$

Complex vector space structure of $\mathbb{C}^n$

Normed additive commutative group structure of $\mathbb{C}^n$

Inner product space structure of $\mathbb{C}^n$ over $\mathbb{C}$

$\mathbb{C}^n$ is a complete space