All Questions
Tagged with hamiltonian time-evolution
179
questions
2
votes
1
answer
52
views
Relationship between unitaries generated by a Hamiltonian and its negative sign
Consider two unitary operations $U_1$ and $U_2$ defined by:
$\partial_t U_1 = -iH_1U_1$ and $\partial_t U_2 = iH_1U_2$
Here, $U_1$ is generated by $H_1$ and $U_2$ is generated by $-H_1$, with the ...
- 83
3
votes
1
answer
287
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Time-evolution operator in QFT
I am self studying QFT on the book "A modern introduction to quantum field theory" by Maggiore and I am reading the chapter about the Dyson series (chapter 5.3).
It states the following ...
- 613
1
vote
2
answers
83
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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 ...
- 23
0
votes
2
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64
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Constant of Motion in Quantum Mechanics for explicit time-dependent Operators
I was studying constants of motion in quantum mechanics, and at first, I don't understand the condition to be a constant of motion. Generally, the temporal variation of an operator $A$ is given by the ...
1
vote
1
answer
80
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How to deal with explicit time dependence in the Heisenberg picture?
I am studying for my test in Quantum Mechanics, and there is something I don't quite understand about the Heisenberg picture and Heisenberg's equation of motion. In the lecture, we derived Heisenberg'...
- 111
0
votes
0
answers
32
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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
0
votes
1
answer
54
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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 ...
- 25
4
votes
1
answer
685
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Why does the Dyson series have a 1/n! factor?
This is the explanation from Wikipedia:
Is there a more rigorous proof or explanation of how reducing the integration region to these sub-regions introduces a $\frac{1}{n!}$ factor? I am confused ...
- 337
1
vote
0
answers
31
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How are propagators for splitting methods applied to time-dependent Hamiltonians derived?
Splitting methods are defined to approximate the solution of the differential equation
$$
y'(t) = (X+Y)y(t), \ \ \ \ \ \ \ t \in (t_0,T) \tag{1}\label{eq:1}
$$
where $X$ and $Y$ are non-commuting ...
- 71
0
votes
2
answers
86
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Connection of a concrete Hamiltonian to the generator of time-translations
In a Quantum-mechanics lecture I am hearing we defined the Hamiltonian of a quantum system (a system with an observer) as the generator of the time translation-operation of the system under ...
1
vote
0
answers
68
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Non-Hermitian Hamiltonian in the Heisenberg Picture
I am trying to study a system whose Hamiltonian, after some transformations can be written as
\begin{equation}
\hat{H} = \hat{N}_1(\omega-i\mu)+\hat{N}_2(\omega +i\mu)+\omega\hat{\mathbb{I}},
\end{...
- 13
0
votes
2
answers
140
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
0
votes
2
answers
98
views
Is the time evolution of the universe cyclic? [closed]
If we can assume that quantum mechanics does not have a bound on its applicability, i.e. there are no inherently classical properties of the universe, we can represent the physical state of the entire ...
1
vote
3
answers
242
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It seems that expectation value of $H$ on coherent states is independent of time? But why?
Let's say the particle is in the state $| \psi(0) \rangle = \exp(-i\alpha p/\hbar) |0 \rangle$, where $p$ is the momentum operator.
I have to show that $| \psi(0) \rangle$ is a coherent state and to ...
- 81
2
votes
1
answer
93
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Changing the time parameter and finding the corresponding hamiltonian
I'm dealing with a problem where I have a (classical) Hamiltonian $H(q,p)$ such that, for any scalar function $f(p,q)$,
$$
\dot{f} = \frac{\mathrm{d} f}{\mathrm{d}t} =\{ f,H \}
$$
If I change the time ...
- 31