All Questions
9 questions
7
votes
1
answer
676
views
What happens to branching in the Many-Worlds Interpretation of quantum mechanics in the limit when Planck's constant goes to 0?
We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why ...
0
votes
1
answer
273
views
How Feynman's path integral lead to least action principle? Math proof needed [duplicate]
I have read about Feynman path integral which leads to classical limit.
It said that because $\hbar \rightarrow 0$ in classical view. The function of path integral $\int e^{\frac{1}{\hbar}f(x)} dx$ ...
4
votes
1
answer
379
views
In what sense a path integral can be approximated by the classical contribution $\exp{[\frac{\mathrm{i}}{\hbar}S_{\text{cl}}}]$?
People often say that the amplitude $K(b,a)$ to go from $a$ to $b$ can be approximated by $$K(b,a) \sim \exp{\left[\frac{\mathrm{i}}{\hbar}S_{\text{cl}}(b,a)\right]},\tag{1}$$
where $S_{\text{cl}}(b,a)...
- 349
2
votes
1
answer
150
views
Why the action is taking phase in considering Huygens principle in matter waves?
From Dirac's remarks
$$\langle x_2,t_2|x_1,t_1\rangle=\exp\left[ \frac{i\int_{t_1}^{t_2}\mathrm dt\, L_{\text{classical}}{\left(\dot{x},x\right)}}{\hbar}\right].$$
How can I conclude from Huygens ...
- 519
2
votes
1
answer
155
views
How I can see that everyday life systems behave classical (from QFT path integrals)?
If I would try to treat macroscopic systems consisting of a super-large number of particles (also when environment is included), I have to compute $2N$-point correlation functions with very large ...
- 3,518
1
vote
1
answer
403
views
Classical Limit of Quantum Mechanics recovered from the Path Integral Formalism
From Zee's Quantum Theory in a Nutshell he explains how the classical limit of quantum mechanics can be recovered from the path integral formalism.
It can be shown that the path integral formalism is:...
- 895
6
votes
2
answers
2k
views
Why does the classical path give the dominant contribution in the path integral?
Why is it that the classical path gives the dominant contribution in the quantum mechanical path integral? How do we understand this?
- 27.2k
4
votes
1
answer
801
views
Classical mechanics from Quantum mechanics
I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator
$$K(x,x_0;t)=\langle x|e^{-i ...
- 12.1k
13
votes
2
answers
5k
views
Classical Limit of the Feynman Path Integral
I understand that in the limit that $\hbar$ goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...
- 951