# 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).

834 questions
Filter by
Sorted by
Tagged with
46 views

### conductivity and Linear response theory in Quantum mechanics [closed]

Hello friends I have seen this formula in Linear response theory but I don't understand what is the role of delta function here I asked ChatGPT and said : This term ensures energy conservation, only ...
88 views

### Does time average induce phase space propability distribution?

Lets say we have a trajectory (positions and momenta) $(x(t), p(t))$ that is the solution of the equation of motion for a system with Hamiltonian $H(x,p)$. For some function $A(x,p)$, the time average ...
56 views

### Inconsistency in transition rate derivation in "Introduction to the Quantum Theory of Scattering" by Rodberg and Thaler

I've been working through the derivation of the transition rate in the book "Introduction to the Quantum Theory of Scattering" by Leonard S. Rodberg and R. M. Thaler (Chapter 8, Section 4 &...
• 466
110 views

### Time evolution keeps a certain product state always a product state. Is there a time-independent factorizable evolution for this state?

I am typically thinking of quantum spin chains in the following of some length $L$. I am OK without any locality in the assumptions on $H$. I have a product state $|\psi\rangle$ and a potentially very ...
• 2,242
1 vote
28 views

### Is it possible for a unitary transformation to align 2 spatially distinct wave packages into 1?

This is mainly meant as a more concise and more general formulation of the problems and realizations occurring to me while thinking about the apparatus I described in this question. The main problem ...
• 1,191
1 vote
82 views

### Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]

I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
113 views

### Experimental constraints on time evolution of quantum states

We have so many experiments on quantum systems; many of those regard superposition principle; tests of probabilities; entanglement; quantum communication protocols; and others are related to ...
• 138
66 views

### Do solutions to the time-independent Schrödinger equation always (for any $V$) form a basis for solutions to the time-dependent equation?

Griffith's "Intro to Quantum Mechanics" shows that for $V(x)=x^2$ and $V(x)=0$, solutions to the SE can be constructed as a linear combination of stationary solutions. But is there a theorem ...
• 1,890
106 views

• 111
25 views

### Time evolution using non-Hermitian (not a PT symmetric) Hamiltonian

I am currently dealing with non-Hermitian hamiltonian and dynamics using it. In general the diagonalizable non-Hermitian matrix might have complex eigenvalues and the eigenvectors may not be ...
• 711
53 views

### Does the Hamiltonian always commute with the Time Evolution Operator?

The time evolution operator $U(t, t_0)$ is given as the solution of the equation $$i\hbar \dfrac{\text{d}}{\text{d}t} U(t, t_0) = HU(t, t_0)$$ whether or not the system is conservative. When the ...
60 views

### Derivation of ODE for $c_n(t)$ in Time-dependent Perturbation Theory [closed]

I'm going through the notes on Time-dependent perturbation theory from MIT OCW and want to make sure I understand how we're going from the first equality to the second in the picture attached below: ...
33 views

### Homogeneity of Schroedinger equation implies norm conservation

I am trying to understand how homogeneity of Schroedinger equation implies norm conservation. I know that we are considering the non-relativistic case, where particle number is conserved, so we do not ...
• 1,396
1 vote
53 views

### Estimate (time dependent) Hamiltonian from given time evolution of a density matrix

Basically the question is, whether you can give some estimation for the Hamiltonian of a system, given the time evolution of a density matrix $\rho$ under the assumption that it obeys the von-Neumann ...
• 11
1 vote
52 views

531 views

### Time Evolution of Eigenkets in the Heisenberg picture

I'm reading Modern Quantum Mechanics by Jun John Sakurai and in section 2.2 he talks about Base Kets and Transition Amplitudes. He goes to show, that $|a',t\rangle=\mathcal{U}^\dagger|a'\rangle$, (...
56 views

• 298
57 views

### Time evolution of mixed state?

Suppose I have a quantum statistical mechanics system in the grand-canonical ensemble. It is given by some Hamiltonian $H = H_{0} + V$, where $H_{0}$ is the free part and $V$ an interaction. The state ...
• 1,123
1 vote
148 views

• 11.9k
1 vote
63 views

### Non-Hermitian Hamiltonian in the Heisenberg Picture

I am trying to study a system whose Hamiltonian, after some transformations can be written as \hat{H} = \hat{N}_1(\omega-i\mu)+\hat{N}_2(\omega +i\mu)+\omega\hat{\mathbb{I}}, \end{...
1 vote
113 views

### Time evolution vs. Time translation in QFT

There is a certain sign mismatch between the time translation operator and time evolution operator in quantum field theory which I hope someone can illuminate. From my understanding, a Poincaré ...
1 vote
153 views

### Fermi Golden Rule: Why interaction picture is fundamental for proving it? [closed]

Sakurai and Wikipedia proove the golden rule in the interaction picture. As the reason of that choice is not clear for me, I ask you what are the difficulties that rise up when you try to get the rule ...
55 views

282 views

• 244
137 views

### Minimal Time for Quantum System to Reach Orthogonal State [closed]

I am trying to determine the minimal time $t$ where a single qubit system (as detailed below) reaches the orthogonal state $|1\rangle$. I have arrived at an answer, but I am not entirely sure whether ...
• 103
### Confusion regarding the $S$-matrix in Quantum Field Theory
In his Harvard lectures on QFT, Sidney Coleman defines the $S$-matrix as, $$S \equiv U_{I}(\infty, -\infty)$$ Where $U_{I}(-\infty, \infty)$ is the time evolution operator in the interaction picture....