Tagged Questions
5
votes
2answers
101 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
90 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 ...
3
votes
2answers
165 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
393 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
117 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
614 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
$$
...
1
vote
4answers
133 views
Why do we consider the evolution (usually in time) of a wave function?
Why do we consider evolution of a wave function and why is the evolution parameter taken as time, in QM.
If we look at a simple wave function $\psi(x,t) = e^{kx - \omega t}$, $x$ is a point in ...
2
votes
5answers
579 views
What does a unitary transformation mean in the context of an evolution equation?
Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real ...
6
votes
2answers
543 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 ...
