# 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).

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### Relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread

Consider a wave packet that satisfies the relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread appreciably in the time it ...
1 vote
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• 167
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### What is the idea behind quantum speed limits?

Could someone please explain to me how the very basic idea behind existence of a quantum speed limit arises? I think I understand (if it's correct) how it arises naturally between two pure states ...
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### Simple time evolution for quantum relativistic particle

I am considering the time evolution of a relativistic particle in 1D, with the time-evolution governed by the equation: \begin{eqnarray} \left(\begin{matrix} \mathrm{i}\partial_{x} && m_{0}\...
• 200
1 vote
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### Are stationary states only eigenstates of $H$?

are stationary states only eigenstates of $H$? If I have an hermitian operator $O$ that commutes with $H$ so that is a constant of motion, are the eigenstates of $O$ also stationary states since a ...
• 601
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### Commuting with the Hamiltonian operators are conserved quantities [closed]

In this question What does "commuting with the Hamiltonian" mean?. I've read that if an operator commutes with the Hamiltonian it is a conserved quantity, this means that the average value ...
• 601
1 vote
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### Can we physically reverse a dispersing Gaussian wavepacket? [duplicate]

A Gaussian wavepacket can be considered a superposition of infinite sinusoidal waves, each with different frequency and amplitude. The propagation velocity of each constituent wave can be frequency ...
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### Unitary time evolution operator and the corresponding Hamiltonian

Could someone tell me how to find the eigenvalues $(E)$ of a time independent Hamiltonian $(H)$ if the eigenvalues of the corresponding unitary time evolution operator $U$ $\left(=e^{itH/\hbar}\right)$...
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### Truncated Completely Positive Trace Preserving (CPTP) maps

Let us consider the the Liouville equation of a level $N$-system with density matrix $\rho$ together with its standard properties (positive semi-definite, unit trace, etc). The evolution of the system ...
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1 vote
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### Varying the Hamiltonians between two fixed states

Let us have a Hamiltonian $H_0$ and 2 states which can time evolve into each other via this Hamiltonian. In this particular situation, say one of the states evolves into the other in time $t_0$ . Now ...
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### Form of the interaction representation time evolution operator

I am a bit confused about the interaction representation picture. Consider the time independent Hamiltonian $H = H_0 + V$. My question concerns the interaction representation time evolution operator: \$...
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