All Questions
Tagged with semiclassical classical-mechanics
12 questions with no upvoted or accepted answers
3
votes
1
answer
64
views
Deriving classical trajectories from quantum mechanics
A paper [1] by David Wallace contains a brief description of how classical trajectories emerge from quantum mechanics. I've summarised the relevant parts below:
Wallace says that decoherence lets us ...
3
votes
0
answers
107
views
Meaning of equations associated with Legendre transform
In the famous paper about semiclassical Bloch theory https://arxiv.org/abs/cond-mat/9511014, the Lagrangian
\begin{eqnarray}
L (\mathbf{k},\dot{\mathbf{k}}) = -e \delta \mathbf{A}(r,t)\cdot\dot{\...
2
votes
2
answers
179
views
Classical limit of quantum harmonic oscillator
I have read that if in the quantum harmonic oscillator, $n$ is very large, then the probability density is similar to the classical one.
In the case of a simple harmonic oscillator:
$$P_{clas}=\frac{1}...
2
votes
0
answers
85
views
Additional Examples of Quantum and Classical Analogs?
I was wondering if there are any other important classical/quantum analogs, along the lines of these examples:
Schrödinger Equation $\leftrightarrow$ Hamilton-Jacobi Formalism
Path Integrals $\...
- 429
1
vote
2
answers
119
views
Why Normalise by $h$ in the Partition Function for Classical Harmonic Oscillator?
I was wondering if anyone could explain the reasoning behind the $h$ normalization constant when calculating the partition function for a classical harmonic oscillator.
I know that the partition ...
- 31
1
vote
0
answers
84
views
Understanding the phrase "Classical mechanics corresponds to the high frequency limit of quantum mechanics"
Recently I have taken an interest in mathematical physics and as my background is mostly in math itself, I have quite a lot of catching up to do regarding my knowledge of physics. One phrase that I ...
- 149
1
vote
0
answers
90
views
Einstein–Brillouin–Keller quantization rule, what does it really mean?
The Einstein–Brillouin–Keller method is a quantization rule going from classical mechanics to quantum mechanics, according to wikipedia:
I have several question regarding the above description:
what ...
- 6,187
1
vote
0
answers
84
views
Algebraic solution of problems in classical mechanics
We know from the theory of the quantum harmonic oscillator that the energy spectrum can be determined nearly effortlessly once we are aware of the simple algebraic structure.
In a certain sense, we ...
- 1,080
1
vote
0
answers
350
views
Using the correspondence principle, how does one show that in the classical limit, the expectation value of $H$ is the classical energy?
I saw an awesome derivation of Schrodinger's equation on Wikipedia. Part of it relies on:
So far, $H$ is only an abstract Hermitian operator in the equation $H\Psi = i\hbar\dfrac{\partial\Psi}{\...
- 2,984
0
votes
2
answers
150
views
How Quantum Mechanics reconciles with Classical Mechanics?
Imagine we have to charged particles. The kinetic energy of the system is:
$$
T = \frac{1}{2}(m_1 + m_2) \mathbf{\dot{R}}_{cm}^2 + \frac{1}{2} \mu \dot{R}^2 + \frac{L^2}{2 \mu R^2}
$$
and its ...
- 1,573
0
votes
0
answers
610
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 ...
- 733
0
votes
0
answers
71
views
Correspondence principle for macroscopic orbits
According to the correspondence principle, quantum laws ought to reduce to classical ones in the limit of macroscopic bodies, right?
But I don't see how the probability clouds of electrons in ...
- 2,984