All Questions
Tagged with oscillators quantum-mechanics
33 questions
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60
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Is it possible that gravitational waves emanating from matter have a "current" flowing in the opposite direction, leading towards the source matter?
In the case of electric current, we consider a conventional direction opposite to the natural movement of electrons. Would it be possible for something similar to happen with gravity? Do gravitational ...
0
votes
1
answer
56
views
Spherical quantum oscillator: Is energy smaller than the potential?
A particle with mass $m$ is inside the spherical quantum well $V(r)$:
\begin{equation}
V(r)=
\begin{cases}
-V_0, & \text{if}\ r<a \\
0, & \text{otherwise}
\end{cases} \...
- 111
1
vote
1
answer
104
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Particle in an oscillating box [closed]
This isn't a question for a class, it's just driven by curiosity.
I hope you like it.
Let's consider a particle in a box with infinite potential barriers, but now the walls can oscillate/move.
Does ...
- 11
0
votes
0
answers
40
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Steady-state of an expectation value of an oscillator system
For context, I am dealing with an equation of motion for the expectation value $\beta=\left\langle\hat{b}\right\rangle$ of a quantum van der Pol oscillator. But I would love a more general explanation....
- 836
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2
answers
155
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Equation of motion of a particle in a sinusoidal well
Do you have solutions for the (classical or not) equations of motion of a particle in a sinusoidal well or just a quartic well, classicaly I would write the equations like so:
$$\frac{d^2x}{dt^2}\...
- 249
1
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0
answers
60
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How do I separate two different creation/ann operators?
$a$ and $b$ are identical systems. The Hamiltonian is given by $H=H_a+H_b =a^\dagger_k a_k +b^\dagger_k b_k$ and these are non-interacting particles.
How do I separate a time dependent operator
$A(t)= ...
- 21
4
votes
2
answers
723
views
In what sense is a quantum damped harmonic oscillator dissipative?
The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains ...
- 27.6k
1
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0
answers
36
views
Intrinsic oscillation
In this paper here
It defines some time scales.in page 3 was said that
$$
\tau_E^{-1}\equiv min |\epsilon_{mn}(t)| \quad ,m \neq n
$$
where $ \epsilon_{mn}(t) ≡ \epsilon_m(t) − \epsilon_n(t)$ denotes ...
- 151
6
votes
2
answers
1k
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Why we can neglect rapidly oscillating terms in favor of slowly oscillating terms?
I never really understood why we can neglect rapidly oscillating terms in favor for slowly ones. As an example, in my quantum-mechanics studies I ran into this ODE:
$$i\frac{d}{dt}\gamma_a = Ae^{i(\...
- 127
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4
answers
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"Natural Frequency" of A Quantum Simple Harmonic Oscillator
This is perhaps a naive question, but I have just recently been introduced to QM so here it goes: we are studying the simple Q.M. Harmonic oscillator. I understand that in the classical picture, the ...
- 435
2
votes
1
answer
97
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Quantising a Damped Mass on a Spring
Background: this question discusses Lagrangian/Hamiltonian formulation of a dissipative problem. However, I'm not clear if this can be made quantum and would like a more explicit roadmap if possible.
...
- 4,584
1
vote
1
answer
121
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Difference between oscillation and radiation?
Im doing this specifically in terms of the Zeeman effect, but in general I have read some stuff about osciallations and orientations that is confusing me. If we have a magnetic dipole, propagating a ...
- 173
1
vote
0
answers
291
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3D harmonic oscillator magic numbers
I know that,
$$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV} $$
and $$E = (n+3/2) \hbar \omega.$$
How do you find the magic numbers of protons and neutrons which ...
- 11
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1
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426
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Quantum Theory: Why Particles Oscillate? [closed]
I understand that as the energy of a particle increases, it oscilates more visciously. I know that there isn’t a consensus on this, but are there any theories out there that explain what causes ...
2
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1
answer
397
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How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule? [closed]
How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?
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