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### 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 ...
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### 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 $\hbar$ ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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?
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### 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 ...
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### 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 ...
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### 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:...
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### 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 ...
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### Star Product and Poisson Brackets

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