# 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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### Proof of quantum correlation functions

I'm reading through David Tong's lecture notes on QFT. On pages 76-77, he gives a proof about correlation functions. See the below link: QFT notes by Tong I'm following the proof steps to obtain ...
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### Time-dependent quantum mechanical picture

As we know,there are three kinds of pictures in quantum mechanics, namely the Schrodinger picture, Heisenberg Picture and also the Dirac picture. If you look at the Wikipedia about the explanation of ...
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### What's the reasons to use time-ordering operator?

I have met the time ordering operator $T$ in many places, such as in the Dyson series $$U(t) = T\exp{\left(-\dfrac{i}{\hbar}\int_0^tdt'H(t')\right)},$$ or in the definition of single particle ...
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### Exactly solvable quantum dynamics problems [duplicate]

By exactly solvable model, people generally mean models whose eigenstates or eigenenergies can be solved analytically. Simple examples are the harmonic oscillator, the infinitely deep square well ...
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### Can the solution to a time-independent Schrödinger equation be considered as a limiting state?

As discussed here, the quantum state $S$ that corresponds to the solution $\psi(t,x)$ of a time-independent Schrödinger equation remains constant wrt. time. I assume that the the solution of a time-...
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### A derivation problem about the Lewis-Riesenfeld theory

I am read the original paper. There is one step I cannot understand. Namely, the highlight sentence below. How to understand $i \frac{\partial }{\partial t}$ as a Hermitian operator? How to prove ...
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### Time evolution of 2-particle states in QFT in the Heisenberg picture

I have a rather basic question about quantum field states. Usually the Heisenberg picture is used in QFT whose effect is that quantum states are time-independent and the operators on the states carry ...
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### Does angular momentum of hydrogen atom imply motion of electron around the nucleus?

Does the non-zero orbital angular momentum (or z-component of angular momentum) of a stationary state of hydrogen atom imply motion of electron (or at least the probability density $|\Psi|^2$) around ...
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### Time resulting of a thermodynamics effect?

I heard in a documentary that : Irreversibility of time is linked to Heat Dissipation in thermodynamics. The theorist says "passage of time" is only a macro sensation, the underlying effect ...
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### Using Dyson formula in Schrodinger picture

From Time-ordering and Dyson series and what I learnt, Dyson formula is used in the situation of interaction picture: $$i\frac{dU_I}{dt} = H_{I}(t)U_I$$ where $H_I(t)$ is interaction Hamiltonian ...
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### Schroedinger Picture more general than Heisenberg Picture?

When thinking about the two pictures, what I found to be strange was: I can write the postulate of time-evolution in the Schroedinger picture by: \begin{align} i \hbar \frac{d}{dt} \lvert \Psi(t) \...
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### Relationship between the Lindblad Equation and Redfield Equation

Both the Lindblad and Redfield Equation both model the open quantum system dynamics given a Hamiltonian and some operators. What is the relationship between the two equations? How can they transformed ...
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### Wave packets in Dirac equation

Gaussian wave packets remain Gaussians after evolution in case of the Schrodinger equation. It is a very useful property of these wave packets. I don't think the same is true for a Gaussian wave ...
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### Time-dependence of density operator in quantum statistical mechanics

I'm struggling to understand a couple of textbook explanations relating to the density operator in quantum statistical mechanics. Firstly, in Huang's book "Statistical Mechanics" it says that "The ...