The time-evolution tag has no wiki summary.
5
votes
2answers
111 views
Quantum Mechanical Operators in the argument of an exponential
In Quantum Optics and Quantum Mechanics, the time evolution operator
$$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$
is used quite a lot.
Suppose $t_i =0$ for simplicity, and say the ...
1
vote
1answer
92 views
Relationship between a formal vector derivative and time evolution of an operator
I'm an undergraduate in physics, with all the lack of knowledge inherent in that. In two of my classes, my professors introduced two equations which look eerily similar. The first, from general ...
1
vote
4answers
134 views
Why do we consider the evolution (usually in time) of a wave function?
Why do we consider evolution of a wave function and why is the evolution parameter taken as time, in QM.
If we look at a simple wave function $\psi(x,t) = e^{kx - \omega t}$, $x$ is a point in ...
3
votes
2answers
166 views
“Inverted” quantum oscillator
I'm trying to understand the problem of the "inverted" oscillator, which has the following Hamiltonian:
$$
\hat{H}=\frac{\hat{p}^{2}}{2m}-\frac{k\hat{x}^{2}}{2}
$$
Suppose that a particle at the ...
5
votes
2answers
404 views
Expectation value of time-dependent Hamiltonian
I'm trying to solve a problem in QM with a forced quantum oscillator. In this problem I have a quantum oscillator, which is in the ground state initially. At $t=0$, the force $F(t)=F_0 \sin(\Omega t)$ ...
2
votes
2answers
118 views
Time evolution of a reduced density matrix
For a bipartite quantum system evolving under some master equation, is the time derivative of the reduced density matrix equal to the partial trace of the time derivative of the matrix?
In other ...
4
votes
1answer
640 views
Evolution operator for time-dependent Hamiltonian
When i studyed QM I'm only working with non time-dependent Hamiltonians. In this case unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation
$$
...
4
votes
4answers
472 views
Can the universe be described by a Markov chain?
This may be a fairly basic question as I don't have a strong background in physics. I intuitively thought that the universe must be able to be described by a Markov chain. That is, I thought you ...
6
votes
2answers
545 views
Equation of motion for the reduced density matrix
The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced ...
3
votes
3answers
180 views
Does the second law of thermodynamics tell me how the entropy changes?
In thermodynamics I can e.g. compute the properties of ideal gases with certain energies $U_1,U_2$ in boxes with certain volumes $V_1$ and $V_2$. Say I have two such boxes and they have some specific ...
2
votes
5answers
594 views
What does a unitary transformation mean in the context of an evolution equation?
Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real ...
