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Results tagged with quantum-mechanics
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user 1287
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
31
votes
Accepted
Evolution operator for time-dependent Hamiltonian
Yes, you are on the right track. The series you have there is called Dyson's series.
First note that the $n$'th term looks like
$$
U_n = \left(-\frac{i}{\hbar}\right)^n\int_0^t dt_1 \cdots\int_0^{t_{n …
- 3,102
23
votes
Quantum mechanics on a manifold
As far as I understand it there are essentially two ways in which you can study quantum mechanics on a manifold with some curvature. Classically speaking these two ways lead to the same physics but in …
- 3,102
10
votes
Accepted
Equation of motion for the reduced density matrix
There are a number of schemes that have been developed over the years to describe the dynamics of the reduced density matrix. The problem that you encounter is that you have to make a choice between c …
- 3,102
5
votes
Accepted
Expectation value of time-dependent Hamiltonian
My approach would be: first determine the time evolution of $\hat{x}(t)$ and $\hat{p}(t)$. For $\hat{x}$ you have
$$
\frac{d}{dt}\hat{x}_H(t) = i[H_H,\hat{x}_H(t)] = \frac{i}{2m} [\hat{p}_H(t)^2,\hat{ …
- 3,102
3
votes
Can the Heisenberg interpretation or path integrals apply to open quantum systems?
Yes, it can.
An example is Brownian motion, in which you are interested in the dynamics of a particle in contact with some external reservoir without being interested in the dynamics of said reservo …
- 3,102
2
votes
Accepted
Isn't it incorrect for the minimal gauge coupling and related calculations in Prof. Ezawa's ...
I have done this calculation some time ago. My convention was:
$$ X = x - \frac{P_y}{m \omega_c}\quad Y = y + \frac{P_x}{m \omega_c} $$
and
$$P_i = p_i +\frac{e}{c} A_i$$
And the magnetic field is …
- 3,102
0
votes
Special relativity version of Feynman's "Space-Time Approach to Non-Relativistic Quantum Mec...
The method introduced here by Feynman is the Path Integral approach to quantum mechanics. When trying to include special relativity, you also need to move from quantum mechanics to quantum field theor …
- 3,102