Linked Questions

18
votes
6answers
4k views

Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
16
votes
5answers
6k views

Classical limit of quantum mechanics

I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ ...
22
votes
2answers
3k views

How do you solve classical mechanics problems with quantum mechanics?

Let's take the very simple problem of what happens if I drop a 1 kg ball from a height of 1 meter. Classically, $F = mg$ and $g \approx 10 \frac{\mathrm{m}}{\mathrm{s}^2}$, so the ball feels a force ...
0
votes
6answers
9k views

Newtonian Mechanics and Quantum mechanics

Why isn't Newtonian mechanics valid in Quantum world? Suppose you isolate an alpha particle and accelerate it in absolute vacuum. Why it doesn't follow the equation $F=ma$? If Newtonian mechanics is ...
15
votes
2answers
2k 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 ...
2
votes
3answers
915 views

Transition from quantum to classical mechanics

As I understand it, if $S \gg h$ then we are in the classical realm, whereas if $S \leq h$ we are in the quantum realm. My question is what happens somewhere in between those 2 limits? Are we quantum ...
0
votes
3answers
2k views

Why do we obtain classical physics by taking the limit of Planck's constant to zero?

Why if we specifically set Planck's constant equal to zero (the limit of it) do we sometimes get classical physics? I mean, what does it mean physically to set the constant equal to zero? Or to say it ...
3
votes
1answer
321 views

Why does the classical path of a particle give the dominant contribution in the path integral?

Why is it that the classical path of a particle gives the dominant contribution in the quantum mechanical path integral? How do we understand this?
2
votes
1answer
511 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 ...
4
votes
1answer
597 views

Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
0
votes
1answer
201 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:...
4
votes
1answer
160 views

Example of a quantum-mechanical theory with nontrivial classical limit

I am looking for a toy model example of a well defined quantum-mechanical theory with the following properties: It can be constructed via canonical quantization starting from some classical theory ...
1
vote
1answer
107 views

Star Product and Poisson Brackets

I have the following definition of star product, \begin{equation} \star=\exp\left[\frac{i\hbar}{2}\left(\frac{\overleftarrow{\partial}}{\partial Q^{I}}\frac{\overrightarrow{\partial}}{\partial P_{I}}-\...
0
votes
0answers
161 views

The classical limit of QM as a Hamilton-Jacobi equation?

I'am having difficulties to understand the so-called classical limit in quantum mechanics. There is a popular method to transform the Schrödinger equation into two coupled equations that are the ...
1
vote
1answer
88 views

Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?

Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit? From undergraduate quantum mechanics, I know that we ...