6
votes
2answers
136 views

Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
1
vote
1answer
129 views

Dirac's remark that inspired Feynman when formulating path integral

When Feynman was trying to formulate path integral of quantum mechanics, he was inspired by Dirac's remark which roughly states that $e^{i\frac{S}{\hbar}}$corresponds to the transition amplitude, ...
5
votes
5answers
207 views

Quantum entanglement and spooky action at a distance

When quantum entanglement is explained in "layman's terms", it seems (to me) that the first premise, that we have to accept on faith, is that a particle doesn't have a certain property (the particle ...
1
vote
1answer
93 views

How do I obtain the Lagrangian in standard for using action? [closed]

I have action as shown below $$S=\int \mathrm{d}t \int \mathrm{d}x^3 \bar\psi\left(i\partial_t\psi +\frac1{2m}\bar\nabla^2\psi-V(x)\psi\right)$$ How do I manipulate it to obtain the Lagrangian ...
3
votes
0answers
58 views

The relation between the action of tunneling and the energy

In the semi-classical physics, the probability of the penetration through a barrier is given by $$ p \sim \exp \left( - A_{0} (E) \right), $$ where $A_0$ is the imaginary part of the action and $E$ ...
1
vote
1answer
206 views

Discretization of action in path integral

I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives: $$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right) dt ~\rightarrow~ \sum ...
4
votes
3answers
773 views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
25
votes
5answers
3k views

Hamilton's Principle

Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ...