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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Phase evolution rates of quantum sub-systems
Do the phases of the wavefunctions for non-interacting quantum systems evolve faster if those systems are conceived of as components within some larger system rather than each being treated separately?...
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Do existing quantum mechanical models provide a physical mechanism for finite-time quantum state transitions?
In standard quantum mechanics, the formalism successfully predicts transition probabilities between quantum states, but the transition itself is often treated as instantaneous or left without a ...
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Does time-ordered exponential still have the BCH lemma?
I am reading Shaul Mukamel's Principles of Nonlinear Spectroscopy. When talking about time evolution in Liouville space, he says in page 61 that
$$\mathscr{U}_{jk,j^\prime k^\prime}(t,t_0)=U_{jj^\...
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Fourier transform of fully nonlinear Heisenberg equations for coupled Kerr modes
I am investigating the dynamics of two interacting bosonic modes with self-Kerr and cross-Kerr nonlinearities. The Heisenberg equations of motion are:
$$
\frac{d\hat a}{dt} = - i\omega_a \hat a + \...
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Instantaneous eigenstates and real solutions of Schrödinger Equation [closed]
As we know, instantaneous eigenstates of energy are the states in which the wavefunction collapses instantly after we measure energy. And we also know that instantaneous eigenstates don't satisfy the ...
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Quantum harmonic oscillator. Application of evolution operator on position eigenstate yields a momentum eigenstate. How to find the phase factors?
Sorry about the stupid title. I have no idea how to summary the following content into a concise title.
This is related to exercise 5.8 of Cohen-Tannoudji's QM textbook.
Let us consider a 1D harmonic ...
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Do maps between pure states of a quantum system correspond to elements of the projective unitary group?
A very standard and widely discussed fact in quantum mechanics is that pure quantum states are only defined up to an overall phase factor.$^1$ That is, the state vectors $|\psi\rangle$ and $e^{i \...
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Confusion about the definition of the interaction-picture potential $V_I(t)$
I am reading a derivation of the interaction picture in subsection 7.2.4 from Schwartz's QFT book, and I am confused about how the interaction-picture potential $V_I(t)$ is being defined and used.
At ...
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Measuring energy (when the potential is time varying)
When the potential is time varying,there are no energy (total energy) eigenstates.So what energies values we obtain when we measure the energy of a particle in such a potential?Does "not having ...
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Why do physical laws depend only on velocity but not acceleration? [duplicate]
Newton's Laws can be presented as a statement regarding the acceleration and time evolution of objects:
$$\ddot {\bf x} = F(\dot {\bf x},{\bf x}) $$
In other words, the time evolution of a physical ...
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How do we define time-ordering operations in QFT?
Given two bosonic operators $A$, $B$ (in the Heisenberg picture) in a QFT, the time-ordered product of $A$ and $B$ is defined as
$$
T\{A(t_1)B(t_2)\}=\theta(t_1-t_2)A(t_1)B(t_2)+\theta(t_2-t_1)B(t_2)A(...
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Dyson series expression for the two-point Green function
On Chapter 7 of Fetter & Walecka, the authors prove Dyson formula for the (imaginary time) propagator $U(t,t_{0}) = e^{H_{0}t_{0}}e^{-H(t_{0}-t)}e^{-H_{0}t}$, where I am ommitting the $\hbar$'s. ...
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Time evolution of mechanical momentum operator in electromagnetic field [closed]
Follow-up question to How to deal with explicit time dependence in the Heisenberg picture?
Time evolution of an operator A (in Heisenberg picture) is given as:
$$\frac{\mathrm{d}\hat{A}_H}{\mathrm{d}t}...
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How to reconcile the reversible nature of microscopic physics with the irreversible nature of macroscopic reality? [duplicate]
This might be a conceptual question more than a technical one, however it would be very useful to see different conceptual approaches to address this problem physically/mathematically.
The question ...
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How to switch from the interaction picture to the Heisenberg picture?
In the Schrödinger, Heisenberg, and interaction pictures, the time evolution of an operator $A$ is defined differently.
In the $\textbf{Heisenberg picture}:$
\begin{equation}
A_H(t) = e^{i(H_0 + V)t} ...
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