1
vote
1answer
88 views

Time evolution of a quantum system

A quantum system has Hamiltonian $H$ with normalised eigenstates $\psi_n$ and corresponding energies $E_n$ ($n = 1,2,3...$). A linear operator $Q$ is defined by its action on these states: $$ ...
2
votes
1answer
95 views

Is continuous evolution from one eigenstate of operator $O$ to another $O$-eigenstate possible?

Eigenvectors associated with distinct values of an observable are orthogonal, according to quantum mechanics. Does this entail that a quantum system cannot continuously evolve from one eigenstate ...
5
votes
2answers
217 views

Quantum Mechanical Operators in the argument of an exponential

In Quantum Optics and Quantum Mechanics, the time evolution operator $$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$ is used quite a lot. Suppose $t_i =0$ for simplicity, and say the ...