All Questions
Tagged with harmonic-oscillator potential-energy
53
questions
-1
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2
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When is minimum potential energy in simple harmonic motion not zero?
We know that in simple harmonic motion, potential energy is minimum at the mean position and it is zero since displacement is zero. So what are some cases in which minimum potential energy is not zero?...
- 91
1
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1
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73
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Quantum Harmonic Oscillator With a Linear "Perturbation"
It is well known that the energy solutions for the unidimensional quantum harmonic oscillator $V(x) = \frac{1}{2}m\omega^2x^2$ are $E_n = (n + \frac{1}{2})\hbar\omega, n \in \mathbb{N}$. In particular,...
- 376
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130
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Why can we ignore the work done by gravity?
I am working through the problem above, starting with part (d). By the conservation of energy setting the spring in equilibrium as $y_0$ as the difference in length of the unstretched spring to the ...
-1
votes
2
answers
59
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Shape of graph of energy in S.H.M
I'm confused to whether the graph of KE/PE of a simple harmonic motion system is sinusoidal or not
those are my best sketches but if unclear, the blue one is in a shape of a sine wave.
this question ...
- 117
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votes
1
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63
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Doubt obtaining the expected value of $x^2$ of a bidimensional harmonic oscillator
Just for the sake of context I'll add a little bit of introductory of the theory we were doing:
Say we are in the context of a bidimensional isotropic harmonic oscillator with an energy found of $2\...
- 75
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90
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Classification of equilibrium configurations for particles subject to elastic force constrained on a circle
I am interested in classifying all the possible equilibrium configurations for an arrangement of $l$ equal point particles $P_1, P_2, . . . , P_l$ $(l > 2)$ on a circle of radius $R$ and centre $O$....
- 130
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votes
1
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32
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Potential, mass and direction of force due to that mass
In the derivative of a potential (which is in the shape of a parabola), is a slope and it has a mass $m$ in the positive slope. Why does the mass tend to exert force in the negative slop direction?
- 3
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133
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Potential energy of a one-dimensional mass
The potential energy of a one-dimensional mass $m$ at a distance $r$ from the origin is $$U(r) = U_0 \left(\frac{r}{R} + \lambda^2\frac{R}{r} \right)$$ for $0 < r < \infty$, with $U_0$, $R$, $\...
- 395
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1
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86
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Schrödinger-Propagator for combined linear and harmonic potential
Given the Hamiltonian
\begin{equation}
H = \frac{p^2}{2m} + V(x)
\end{equation}
The propagator for a pure harmonic potential of the form
\begin{equation}
V(x) = \frac{1}{2} m \omega^2 x^2
\end{...
- 141
1
vote
1
answer
61
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Elastic potential energy in vertical simple harmonic motion
When we calculate gravitational potential energy, we use a reference point as a zero-line. That is, we set the gravitational potential energy to zero at a specific point (usually the ground). Now, ...
- 71
1
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1
answer
62
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Potential energy of phonons as harmonic oscillators
I'm trying to derive the phonon hamiltonian which is anologous to a collection
of independent harmonic oscillators. I've already have kinetic energy but I'm kinda stuck on the potential energy. The ...
- 333
1
vote
1
answer
151
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Vanishing zero point energy in harmonic oscillator
In classical mechanics, adding a constant to the potential changes nothing. In quantum mechanics, this just shifts the energy and multiples the wavefunction with a phase term.
But now suppose I use ...
- 1,931
1
vote
2
answers
94
views
Why doesn't $\omega = \sqrt{\frac{U''(x_0)}{m}}$ work for a simple pendulum?
In a simple pendulum, we know that the angular frequency of small oscillations is $\omega = \sqrt{\frac{g}{l}}$. However $\sqrt{\frac{U''(x_0)}{m}}$ gives $\sqrt{gl}$ as the angular frequency.
Let $l$ ...
- 23
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votes
1
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332
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Doubt from Arnold; Mathematical methods of classical mechanics (page 20)
I am trying to do a problem from Arnold; Mathematical methods of Classical mechanics.
But I didn't get the desired result mentioned by the author.
Let $E_0$ be the value of the potential function at ...
- 23
1
vote
3
answers
892
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Simple proof that average kinetic equals average potential energy in quantum harmonic oscillator
Is there a simple way to explain why the expectation of the kinetic energy equals the one of the potential energy in the quantum harmonic oscillator? I would like to find a simpler explanation than ...
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