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Tagged with harmonic-oscillator quantum-mechanics
813
questions
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Article on 1D deformed quantum harmonic oscillator
Few years ago I was reading an article which I'm trying to find for quite some time but with no success so far. It was a paper about deformation of 1D quantum harmonic oscillator with continuous ...
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votes
1
answer
71
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How is the quantum harmonic oscillator related to Fock states?
The question is basically in the title.
From what I understand, in the Fock state there is a certain number of particles in each energy level. The creation/annihilation operators create or destroy a ...
- 159
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vote
1
answer
60
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Potentials increasing faster than harmonic oscillator
I'm reading a book which says: (HO stands for harmonic oscillator):
The spectrum of the HO has equidistant energy eigenvalues. A potential that increases quicker than the HO has states which become ...
- 369
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1
answer
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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} \...
- 109
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votes
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answers
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Understanding the dynamics of a perturbed quantum harmonic oscillator system
I'm trying to understand how quantum systems behave when they are perturbed, and I'm using the quantum harmonic oscillator as a model.
I start by implementing a symmetric gaussian shaped bump in the ...
- 21
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vote
2
answers
54
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Infrared regularizing the harmonic oscillator path integral
This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
- 11
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1
answer
46
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Regarding to the asymptotic solution of quantum harmonic oscillator
In quantum mechanics, the radial equation of the SHO takes the form
\begin{align}
\frac{d^2 u}{dx^2}+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u=0,
\end{align}
where $x=\sqrt{\frac{m\omega}{\hbar}}r$...
- 27
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Can a harmonic oscillator never be Raman active?
Assuming we have some harmonic oscillator
\begin{equation}
H = \omega_0 (a^\dagger a + \frac{1}{2}) = \frac{p^2}{2m} + k x^2
\end{equation}
for which the excitations have even wavefunctions $\Psi_n(x)=...
- 21
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votes
2
answers
59
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Closed expression for expected values of $\hat{p}\,\,^{2j}$ for the vacuum state
I am wondering if there is a closed expression for the expected value $\left<0\lvert \hat{p}\,\,^{2j}\lvert 0\right>$ with $j\in\mathbb{N}$, where $\left|0\right>$ is the vacuum state of the ...
- 219
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3
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Quantum harmonic oscillator meaning
Imagine we want to solve the equations
$$
i \hbar \frac{\partial}{\partial t} \left| \Psi \right> = \hat{H}\left| \Psi \right>
$$
where $$\hat{H} = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial ...
- 221
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vote
1
answer
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Quantum Harmonic Oscillator With a Linear "Perturbation"
It is well known that the energy solutions for the unidimensional quantum harmonic oscillator $V(x) = \frac{1}{2}m\omega^2x^2$ are $E_n = (n + \frac{1}{2})\hbar\omega, n \in \mathbb{N}$. In particular,...
- 376
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votes
1
answer
464
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Physical meaning of Zero-Point Energy
I know that a quantum system can never have 0 energy due the Uncertainty Principle, and its lowest energy is called the Zero point Energy. However, Energy is a relative quantity (atleast in classical ...
- 93
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vote
1
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Question regarding the half Harmonic Oscillator
In the normal Quantum Harmonic Oscillator (QHO), we normally use the operator method (because it's to elegant), but I recently discovered the problem in Griffiths (prob 2.42) where they ask the same ...
- 585
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How can you have position basis and energy basis? [duplicate]
In Quantum Mechanics, my understanding is that we have a Hilbert space.
If we to model a particle in space we consider the space defined by the basis
$$|x\rangle$$
for each $x \in \mathbb{R}$
We then ...
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How can one "encode" momentum into the wave-equation of a QM harmonic oscillator? [duplicate]
I am learning about Quantum Mechanics using Griffiths book and after reading the section about the quantum harmonic oscillator, I was left wondering how one can construct a solution to the Schrodinger ...
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