## How is time calculated in evolution?

The evolution from the time t0 to a later time t2 should be equivalent to the evolution from the initial time t0 to an intermediate time t1 followed by the evolution from t1 to the final time t2, i.e. U(t2,t0) = U(t2,t1)U(t1,t0), (t2 > t1 > t0).

## Does the time evolution operator commute?

Yes. For a given system, there can be lots of operators that commute with the time evolution operator.

**Is the time evolution operator unitary?**

In quantum mechanics, the propagators are usually unitary operators on a Hilbert space. The propagators can be expressed as time-ordered exponentials of the integrated Hamiltonian.

**What is the role of time in evolution?**

The concept of immense periods of geological time are necessary to account for the possibility of the small changes resulting slowly into major changes. Thus long periods of time are essential for Darwin’s theory of slow uniform biological changes being responsible for the Origin of the Species.

### What is rotation operator?

Rotation operator may refer to: An operator that specifies a rotation (mathematics) Three-dimensional rotation operator. Rot (operator) aka Curl, a differential operator in mathematics.

### What is time-dependent perturbation theory?

Time-dependent perturbation theory, developed by Paul Dirac, studies the effect of a time-dependent perturbation V(t) applied to a time-independent Hamiltonian H0. Since the perturbed Hamiltonian is time-dependent, so are its energy levels and eigenstates.

**Can Hamiltonian be time-dependent?**

Dynamical processes in quantum mechanics are described by a Hamiltonian that depends on time. In principle, the time-dependent Schrödinger equation can be directly integrated choosing a basis set that spans the space of interest.

**Why does time evolve unitary?**

That the time evolution operator is unitary, is equivalent to the Hamiltonian being Hermitian. Equivalently, this means that the possible measured energies, which are the eigenvalues of the Hamiltonian, are always real numbers.

#### What period of evolution are we in?

Our evolutionary path takes us through the Pliocene, the Pleistocene, and finally into the Holocene, starting about 12,000 years ago. The Anthropocene would follow the Holocene.