Linked Questions

3
votes
4answers
6k views

Can Newton's laws be explained by Quantum Physics? [duplicate]

I have only basic knowledge of physics. Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels? I'm having ...
3
votes
2answers
2k views

From Quantum Mechanics to Classical Mechanics [duplicate]

Is it possible, and has it been attempted, to use quantum mechanics to deduce Newtonian, macroscopic level mechanics laws as was the case of statistical mechanics deriving thermodynamic relations?
0
votes
0answers
721 views

Can the laws of classical mechanics be derived from quantum mechanics? [duplicate]

Can classical mechanics be derived from quantum mechanics as the same way thermodynamics derived from statistical mechanics?
1
vote
0answers
295 views

How to prove Newton's second law with quantum mechanics? [duplicate]

Newton's second law claims that $F=ma$. In terms of quantum mechanics, the equality can be written as $ \frac{d\langle p \rangle}{dt} = -\langle \nabla V(x) \rangle$. How can I prove this with non-...
0
votes
1answer
227 views

How to go from Quantum World to Classical World? [duplicate]

Possible Duplicate: Is it possible to recover Classical Mechanics from Schrödinger’s equation? Classical Limit of the Feynman Path Integral In the quantum world we don't have specific ...
17
votes
5answers
7k 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 $\hbar$ ...
23
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 ...
17
votes
4answers
1k views

When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?

Lets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation $U(x_{b},x_{a}) = \int_{x_{a}}^{x_{b}} \...
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 ...
7
votes
3answers
3k views

Classical Limit of Schrodinger Equation

There is a well-known argument that if we write the wavefunction as $\psi = A \exp(iS/\hbar)$, where $A$ and $S$ are real, and substitute this into the Schrodinger equation and take the limit $h \to 0$...
14
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 ...
4
votes
4answers
1k views

Classical Limit in Quantum Mechanics

Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will ...
-1
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 ...
5
votes
1answer
1k views

Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything? [duplicate]

Assuming that I learn Quantum Mechanics first, and then I approach Classical Mechanics as a special case of Quantum Mechanics, I will definitely find the relationship between Quantum Mechanics and ...
2
votes
1answer
558 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 ...

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