https://github.com/qojulia/secondquantizedalgebra.jl

Symbolic computations with second quantized operators
https://github.com/qojulia/secondquantizedalgebra.jl

computer-algebra-system hamiltonian quantum quantum-mechanics symbolics

Last synced: 3 months ago
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Symbolic computations with second quantized operators

• Host: GitHub
• URL: https://github.com/qojulia/secondquantizedalgebra.jl
• Owner: qojulia
• License: mit
• Created: 2025-06-03T08:40:46.000Z (4 months ago)
• Default Branch: main
• Last Pushed: 2025-07-19T20:24:53.000Z (3 months ago)
• Last Synced: 2025-07-19T22:59:11.226Z (3 months ago)
• Topics: computer-algebra-system, hamiltonian, quantum, quantum-mechanics, symbolics
• Language: Julia
• Homepage: https://qojulia.github.io/SecondQuantizedAlgebra.jl/
• Size: 419 KB
• Stars: 5
• Watchers: 3
• Forks: 1
• Open Issues: 5
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# SecondQuantizedAlgebra

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A Julia package for symbolic manipulation and algebraic computation with second quantized operators. SecondQuantizedAlgebra.jl provides a flexible framework for working with creation and annihilation operators, commutation relations, and algebraic expressions common in quantum many-body theory and quantum optics.

The package provides:

- Symbolic representation of bosonic fock creation and annihilation operators

- Automatic (anti-)commutation relation handling

- Algebraic simplification and normal ordering

- Support for atom and spin operators

- Extensible for custom operator types

The code was refactored out of [QuantumCumulants.jl](https://github.com/qojulia/QuantumCumulants.jl).

### Installation

Install with Julia's package manager:

```julia

pkg> add SecondQuantizedAlgebra

```

### Usage

```julia

using SecondQuantizedAlgebra

using SymbolicUtils

ha = NLevelSpace(:atoms,2)

hc = FockSpace(:cavity)

h = hc ⊗ ha

@qnumbers b::Destroy(h)

σ(i,j) = Transition(h,:σ,i,j)

@cnumbers g Δ

H = Δ*b'*b + g*(b*σ(2,1) + b'*σ(1,2))

@show b*b'

@show σ(2,1)*σ(1,1)

simplify(commutator(H, b))

```

See the [documentation](https://qojulia.github.io/SecondQuantizedAlgebra.jl/) for more details and advanced usage.

## Contributing

Contributions and suggestions are welcome! Please open issues or pull requests on [GitHub](https://github.com/qojulia/SecondQuantizedAlgebra.jl).

## License

This project is licensed under the MIT License.