# Quantum Objects (Qobj)

**Quantum objects** (`Qobj`) are the fundamental data structure in QuTiP, representing quantum states (kets, density matrices) and operators (Hamiltonians, measurement operators). A `Qobj` stores a matrix and metadata: dimensions, shape, and whether it's a ket, bra, operator, or superoperator.

Every QuTiP calculation uses `Qobj`s. Create them from numpy arrays, use built-in functions (`basis()`, `sigmaz()`, etc.), or import from other formats. QuTiP handles the linear algebra automatically.

```python
from qutip import *
import numpy as np

# Create a ket (column vector) for a two-level system
psi = basis(2, 0)  # Ground state
print(psi)  # Qobj with dims [[2], [1]]

# Create an operator (density matrix)
rho = psi * psi.dag()  # Outer product: |ψ⟩⟨ψ|
print(rho)  # dims [[2], [2]]

# Built-in operators
H = sigmaz()    # Pauli Z
X = sigmax()    # Pauli X
print(H * psi)  # Apply operator to state
```

`Qobj` automatically tracks dimensions, enabling safe composition of multi-qubit systems. Arithmetic operations (addition, multiplication, tensor products) work intuitively on `Qobj`s.

## Qobj Properties

Access components: `.full()` returns the numpy array, `.dims` gives dimensions, `.shape` is the matrix shape. Check `.type` to distinguish kets, operators, etc.

```python
psi = basis(2, 0)
print(psi.full())        # [[1.], [0.]]
print(psi.dims)          # [[2], [1]]
print(psi.isherm)        # False (ket is not Hermitian)

rho = psi * psi.dag()
print(rho.isherm)        # True (density matrix is Hermitian)
```

`Qobj` is the interface between QuTiP and your physics. Master every operation on `Qobj`s—they're the foundation of all simulations.