# Questions tagged [time-evolution]

The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-independent Hamiltonians, the time evolution operator is simply exp(-iHt).

352 questions
Filter by
Sorted by
Tagged with
77 views

### A fundamental question about Time-dependent Hamiltonians

I have a fundamental question about Quantum Mechanics or even mechanics in general. I am aware that there are stationary solutions and non-stationary solutions. The stationary solutions solve ...
151 views

179 views

### Quantum Mechanics - time evolution after a measurement?

A non-degenerate two-level system is described by a Hamiltonian $\hat H$ with $\hat H|n\rangle = \epsilon_n|n\rangle$, where $n = 1, 2$. An observable $\hat B$ has eigenvalues $\pm 1$, with the ...
25 views

### How to describe time dependence piece of a stationary state with average phase

I am reading this paper on the synchronization of atomic clocks via entanglement (https://arxiv.org/pdf/quant-ph/0004105.pdf) and can't figure out how they are using $\Omega = (E_{1} - E_{o})/\hbar$ ...
37 views

### A shaped pulse as a sum of rectangular pulses

I have a pulse with lineshape $L(ω)=\frac{1}{π}\frac{\frac{1}{2}Γ}{((ω−ω_0)^2+(\frac{1}{2}Γ)^2)}$ in the frequency domain where $\Gamma$ is the pulse width and $\omega_0$ is the resonant frequency ...
26 views

2k views

### Why is the momentum-space wavefunction for a free particle not a function of time?

Suppose the initial wave function of a free particle is given by $\psi(x,0)$. Now to find how the wave function evolves with time we generally do the Fourier transform of the wave function at $t=0$. ...
152 views

### Time evolved density matrix

Working with an uncoupled harmonic oscillator Hamiltonian: $H = H_A + H_B$, where $H_A = \hbar \omega (a_+ a_{-} + 1/2 )$ and $H_B = B \sigma_z$. I'm trying to calculate the density matrix $\rho (t)$...
77 views

### Time evolution operator of Klein-Gordon field

If $U(t)=e^{itH}$ is the time evolution operator. And $|\phi \rangle$ is a state of a field at particular time $t_1$ and $|\phi' \rangle$ is the state of a (free) Klein Gordon field at a time $t_2$. ...
138 views

### Origin of the Schrodinger equation by L. D. Landau and E. M. Lifshitz

In the book "Quantum Mechanics" by L. D. Landau and E. M. Lifshitz, it is mentioned that, "The wave function Ψ completely determines the state of a physical system in quantum mechanics. This means ...
Suppose I know the time evolution of an operator is given by $\dot{\hat{O}} = \frac{i}{\hbar}[\hat{H}(t), \hat{O}(t)]$. Now I want to look at a function $\hat{f}(\hat{O}$, and I want to know the time ...
In the Heisenberg picture, I can define the velocity Operator $\hat{V}$ as the operator which satisfies $\hat{V}(t) = \frac{\partial \hat{x}}{\partial t}(t)$ for all $t$. The Heisenberg equation then ...