All Questions
Tagged with stability quantum-mechanics
30 questions
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Stability with the Variational Principle
In quantum mechanics you can use the variational principle to find an approximate bound to the energy of some state. My lecturer said that with this method the stability of an $H_2$ atom and a $H^+$ ...
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Why are orbitals are stable even though they have wierd shapes?
I'm curious to know about why are they stable, let's talk about $p$-orbital , $p$-orbital is dumbbell shaped shouldn't electrons just fall into the nucleus because we need a centrifugal force to ...
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Applying Kato-Rellich to the hydrogen atom model to prove stability of first kind [closed]
Trying to Understand the lower bound on the Schrodinger Operator of the Hydrogen atom. Using the kato-rellich theorem. My education has been in physics and i am slowly adding to my mathematics toolset....
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How much does quantum uncertainty contribute to the uncertainty of earthquakes?
More abstractly, the topic is: amplification of quantum uncertainty within dynamically unstable systems.
I'd like to have a calculable toy model, e.g. maybe a quantum version of the famous "...
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Where does this (hydrogen molecule energy) graph come from?
I was thinking about the good old question of 'Why do molecules have lower energy than the atoms?'
And in a video (around 6:15), this good old energy graph is shown, which is stated as the 'answer' to ...
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Were there any explanations as for the stability of matter before the advent of quantum mechanics?
Reading the paper by Lieb "The stability of matter", it is clear from the start that quantum mechanics is absolutely necessary to solve this problem. However, I assume this question was ...
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Are atoms still unstable in 4 spatial dimensions when the physical size of nuclei is accounted for?
Per this answer, depending on a dimensionless parameter hydrogen atoms in 4 spatial dimensions can be either unbound (i.e., nonexistent), stably bound dependent on boundary conditions, or unstable ...
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What is a quasibound state and how is it different from a bound state?
What is a quasibound state and how is it different from a bound state?
I have read this term in nuclear physics in the context of compound nucleus formation. A compound nucleus $C$ is formed by the ...
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How to show that an atomic Hamiltonian spectrum is lower-bounded?
I'm looking for a proof that the spectrum of an atomic (or molecular) Hamiltonian is lower-bounded.
Right now, the closest I've got is the proof in [1] that the spectrum of a second-order elliptic PDE ...
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3
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Planetary model of the atom
Wherever I look about the early planetary model of the atom, it says the electron must lose energy while revolving around the nucleus. And therefore fall into the nucleus. Thus, the atom is unstable.
...
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Is there a quantum analogue of the "Tennis Racket" theorem?
A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is ...
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Stability of energy levels in quantum mechanics
Does QM explain the fact that in nature electrons in atoms tend to be in the lowest energy level?
Why are excited states unstable? And are excited states always more energetic than stable ones?
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How do electrons stay in orbitals in Bohmian Mechanics?
I've been reading various realist interpretations of quantum mechanics and in Bohmian Mechanics, I found that the "wave" aspect of a quantum particle is removed from the particle to preserve ...
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How Bohr's model explains the stability of atoms?
How Bohr's model explains the stability of atoms? From Maxwell's equation, we know that an electron or any other charge will radiate energy on acceleration.
This problem is said to be solved by Bohr ...
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How is Schrodinger's model of atom consistent with reference to Maxwell's Theory of Electromagnetic Radiation? [duplicate]
When Rutherford proposed his model of atom, he mentioned that "Nucleus is surrounded by electrons that move around the nucleus with very high speed in circular paths called orbits. James Maxwell ...
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Stability/decay, are they boolean or not, or does QM probabilities overrule this?
This is not a duplicate, I am not asking whether the proton is a stable particle, or why it is. I am asking about the definition of stability/decay whether it is boolean or not.
I have read this ...
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Stability condition of a finite difference algorithm
While studying finite difference methods of TDSE I found myself stuck on a reasoning step:
The largest possible spatial curvature for the wave function, $\frac{\partial^{2}}{\partial x^{2}} \Psi(x, ...
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Why exactly is Neutronium-4 unstable and how to explain Marqués' experimental results?
Wikipedia states:
A tetraneutron is a hypothetical stable cluster of four neutrons. The existence of this cluster of particles is not supported by current models of nuclear forces. There is some ...
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Frequencies associated with boson/fermion operators
For a Hamiltonian like,
$$\hat{H}=\sum_{k}\hbar\omega_{k}b_{k}^{\dagger}b_{k}$$
What does it mean to say that the frequencies $\omega_{k}$ must be positive if $b_{k}$, $b_{k}^{\dagger}$ are boson ...
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thermodynamics and stability
Suppose this three processes, at same T and P, each of them on thermodynamical equilibrium:
atoms -->molecule 1
atoms --> molecule 2
atomsdifferent --> molecule 3
Where atoms are infinitely ...
user153036
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Dzhanibekov effect in quantum systems
Dzhanibekov- or Tennis racket effect is what happens when an object with three diferent moments of inertia doesnt spin around the axis with highest or lowest moment of inertia.
The object starts to ...
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(No) imaginary frequency particle oscillations
Suppose we have two scalar fields $\varphi, \kappa$. Next, suppose there is a region in space where they are mix with each other, i.e., we have a lagrangian
$$
\tag 1
L_{\text{int}} = A \varphi \kappa
...
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The stability of an atom
I've read about different models of atom proposed in 18$^{th}$ and 19$^{th}$ centuries, of which the most vital were JJ Thomson's model, followed by Rutherford's nuclear model and then Bohr's quantum ...
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Schrödinger equation solutions: stability and oscillations
What is known about
Stability of solutions of time-independent Schrödinger equation (TISE)?
Existence of time dependent but oscillatory solutions (of Schrödinger equation)?
Stability of oscillatory ...
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2
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Is physics qualitatively stable if we let Planck's constant tend to zero?
I realise that we can't meaningfully answer the quesition "what is Planck's constant were zero" because it would break out physical models beyond recognition.
However, if we let Planck's constant ...
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Is it okay to put singularities into the wave function to test behavior around unstable potentials? [closed]
$$
\psi(r)=\sqrt[4]{\frac{ a}{8\pi^3 }}\frac{ \exp (-a r)}{r^{1.25}}
$$
The wave function above is an example of a function that is normalizable in 3D space and $r=\sqrt{x^2+y^2+z^2}$.
$$
-\psi ''(r)...
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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?
I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance.
Am I ...
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2
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783
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Notions of "confined" and "metastable" states?
What is the exact definition of terms "confined state" and "metastable state", in the context of quantum mechanics?
Can we also have a "confined metastable state"?
Can we somehow easily link these ...
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Possibility of stable muonic structures?
In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it ...
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Where did Schrödinger solve the radiating problem of Bohr's model?
One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would ...
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