Questions tagged [harmonic-oscillator]
The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)
I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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Using perturbation theory or small oscillation approximation in Harmonic oscillator
Let us assume, we are given the following potential,
$$V(x)=\frac{1}{2}ax^2-2x+\epsilon x^3$$
We need to find the energy levels of a particle bound in this potential
Let us think of the ground level ...
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Experimental time-series for quantum particle-in-a-box or simple harmonic oscillator?
I would like to see experimental results for repeated measurement of a single-particle, quantum system that is approximately either particle-in-a-box or simple harmonic oscillator. If particle-in-a-...
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Ground state of harmonic oscillator moving with constant velocity
This post primarily concerns my confusion regarding time-dependent Hamiltonian.
Let's think about a ball resting at the center of a harmonic oscillator potential. Now view the problem in a reference ...
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Why does metaplectic correction fix the vacuum energy?
In geometric quantization we want to go from a symplectic manifold $\left( M, \omega \right)$ to a Hilbert space $H$. If $M$ is prequantizable, we find a prequantum bundle $L \rightarrow M$ with ...
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Cubic perturbation to coupled quantum harmonic oscillators
I recently came across this two-dimensional problem of a particle in a potential of the form
$$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$
where $x$ and $y$ are known ...
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Energy Levels of 3D Isotropic Harmonic Oscillator (Nuclear Shell Model)
One simple way of detailing the very basic structure of the nuclear shell model involves placing the nucleons in a 3D isotropic oscillator. It's easy to show that the energy eigenvalues are $E = \...
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Zero-point energy amplitude calculation
On this page
https://www.miniphysics.com/simple-harmonic-oscillator.html
It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is
$
E = K + U
$
or rather
$
\\
E = \...
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Almost all Liouville torus is preserved for small oscillation problems even if we don't use second-order approximation to potential energy, right?
In small oscillation problems, we use a second-order approximation to the potential energy function (suppose the oscillation is around the point $(0,\cdots, 0)$),
$$
V(x) = V(0) + \frac{\partial^2 V(0)...
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Is there a spatial representation of the fermionic harmonic oscillator?
An answer to another question derives a Hamitonian of the fermionic harmonic oscillator in terms of a pair of position-like and momentum-like operators. These operators are, as expected, defined in ...
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What are the maximum spring lengths of a double spring pendulum?
NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram
For a single spring, you can simply equate ...
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Modelling a pendulum with physical restrictions on it's range of motion
I'm currently working on a project based on suspension bridges and their oscillations. I've got an equation of motion for the movement of a pendulum as shown in the first image, I then wanted to be ...
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QFT-Style Lagrangian for a system of two symmetrized bosons
I'm wondering if anybody may have suggestions regarding the following problem. The Hamilton operator of the quantum harmonic oscillator (QHO) can be written as follows:
$$ \hat{\mathcal{H}}_{QHO} = \...
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The Hamiltonian for clocks?
I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators.
The simplest thought model I am looking for is a formal representation of a clock (for ...
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Lie symmetries of differential equation and ladder operators
There is literature on the lie symmetries of quantum harmonic oscillator differential equation. The generators satisfy certain lie algebra.
On the other hand, we have ladder operator method. The ...
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