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Questions tagged [ground-state]

The ground state of a quantum/classical mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. When a quantum system has infinite possible ground states, it is gapless with massless modes; if a quantum system has finite ground states, it is known as gapped and potentially topologically ordered. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

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Finding the classical antiferromagnetic ground state for the Kagomé lattice

I am attempting to do the following exercise in Altland and Simons Condensed Matter Field Theory: "Show that the classical antiferromagnetic ground state of the Kagomé lattice – a periodic array ...
zeroknowledgeprover's user avatar
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Relationship Between Ground State Wavefunctions' Amplitudes Under Discrete Symmetry Operations

$\newcommand{\ket}[1]{\left|#1\right\rangle}$ Given a Hamiltonian $\hat{H}$ and a discrete symmetry $\hat{T}$, it's known that $\hat{T}\ket{\psi_{GS}}$, where $\ket{\psi_{GS}}=\sum_\sigma \psi_{GS}(\...
Andy Liu's user avatar
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How to get a lower bound of the ground state energy?

The variational principle gives an upper bound of the ground state energy. Thus it is quite easy to get an upper bound for the ground state energy. Every variational wave function will provide one. ...
poisson's user avatar
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Radiation reaction in the ground state of an atom [duplicate]

In a typical bound energy eigenstate of an atom the magnitude of the wave function is time independent only phase changes in time. So I expect no radiation reaction force in the ground state. However ...
atilla gurel's user avatar
2 votes
1 answer
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Why is the "decision" version of the local Hamiltonian problem promised to have a positive gap?

The Wikipedia article on the local Hamiltonian problem is ungrammatical and unclearly written. I think that this is what it is supposed to say: The decision version of the $k$-local Hamiltonian ...
tparker's user avatar
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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,...
Victor Lins's user avatar
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Why is helium in excited state with $S = 1$ more stable than $S = 0$? [closed]

In molecular physics, we were told that helium is more stable with total spin $S = 1$ than $S = 0$, so with $1s^12s^1$. I don't understand why.
Emmannuelle_Legolas's user avatar
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Is the overall (distinguishble-particle) ground state for a many-body identical particle Hamiltonian also immediately the bosonic ground state?

Consider the following many-body Hamiltonian of $N$ particles in an external trapping potential with inter-particle interactions: \begin{align} \hat{H}= \sum_{i=1}^{N} \left[-\frac{\hbar^2}{2m} \...
Coffee-7's user avatar
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How to Calculate the Case of $t=0$ in the $t$-$V$ Model?

In the $t$-$V$ model, the Hamiltonian is defined as: \begin{equation} \hat H = -t \displaystyle \sum_{\langle i,j\rangle} ( \hat c_i^{\dagger} \hat c_j + \hat c_j^{\dagger} \hat c_i) + V \sum_{\langle ...
relaxon's user avatar
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Algebraic definition of ground state

I'm currently studying arXiv: 1706.09666 [math-ph]. On page 51, the authors define what is a ground state in the algebraic approach. I quote them below. If a state $\omega$ is invariant under a one-...
Níckolas Alves's user avatar
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Uniquness of the vacuum in a theory with/without mass gap

Context I read the note Light Cone Quantization and Perturbationwritten by Guillance Beuf. He gives a argument in section 3.3.2, p17, 2nd paragraph : In particular, in a theory with a mass gap, ...
Steven Chang's user avatar
2 votes
1 answer
159 views

Intuition for ground state degeneracy of Majorana checkerboard model

I'm now trying to learn about Fracton. In the very early paper studying Majorana checkerboard model, it is claimed that the ground state degeneracy ${D_0}$ on ${L \times L \times L}$ 3-torus is ${...
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Hamiltonians with collective quantum spins and their ground states

This feels like it could be a undergrad/grad-school quantum mechanics course level problem, or potentially something pretty interesting. I'd be happy with either answer, but I don't know which one is ...
Jun_Gitef17's user avatar
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Confusion on Hamiltonian unbounded from below and Ostrogradsky Instability

This might be a silly question but I failed to get it. In Ostrogradsky Instability, we deduced that Lagrangian of higher-order derivatives leads to Hamiltonian linear to canonical momenta, and thus, ...
Aimikan's user avatar
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Questions of lower boundness of Hamiltonians in quantum theories

In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like ...
6 votes
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Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?

I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
user1792605's user avatar
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Diagonalize a many-body Hamiltonian

Assume we start with a generic many-body Hamiltonian: $$ H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k. $$ Now if there is only the one-body part, which ...
ZhiYu Fan's user avatar
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Expectation value of non-interacting groundstate

Assume that I have a tight binding model given in second quantized form as follows; \begin{equation} H = \sum_i f_i^{\dagger}f_i + t \sum_{i,j} f_i^{\dagger}f_j \end{equation} In real space, ...
zagor's user avatar
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On the existence of ground state for a free particle

Given a free particle, the ground state of the system is the eigenstate with zero momentum. However, we also know that momentum operator does not have proper eigenstates, but rather it's spectrum is ...
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What is the ground state energy of $H = H_{0}-\mu N$?

Suppose we take $\mathscr{H} = L^{2}(\Lambda)$ our one-particle space, with box $\Lambda = [-L/2,L/2]^{d}\subset \mathbb{R}^{d}$ for some $L > 1$. Let $H_{0}$ denote the kinetic energy: $$H_{0,1} = ...
MathMath's user avatar
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Problem about the ground state energy calculated with quantum Monte-Carlo

There are many quantum Monte-Carlo methods. Many of them can be used to calculate or estimate the ground state energy. The problem is, is the estimated energy an upper bound of the true ground state ...
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Non-degeneracy of the ground states of quantum spin models

It is known that the ground state of some quantum spin models is non-degenerate. For example, the ground states of the quantum Ising model and the ferromagnetic Heisenberg model on the subspace of a ...
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Symmetry of the non-degenerate ground state

From Quantum field theory and condenced matter by Shankar, pp67, he mentioned that In normal problems, the symmetric state, or more generally the state with eigenvalue unity for the symmetry ...
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Why does the variational method simplify in this way when $H$ Hermitian?

Ballentine (Quantum Mechanics: A Modern Development 2nd edition, page 290) writes the attached in his introduction of the variational method. My question is about his very last line: why does $H$ ...
EE18's user avatar
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Lower bound on the ground state of 2D s-wave with a radial potential

Consider a Hamiltonian $H = -\Delta + V(r)$ in two dimensions, i.e. $L^2(\mathbb{R^2})$, where $V(r)$ is a smooth and bounded radial and non-positive potential. Let me define $\phi(r)$ as my wave ...
Re_Born's user avatar
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Relation between ground state energy and the potential

I am given the following Hamiltonian: $$H = \frac{p^2}{2m} + \lambda|x|^3$$ where $\lambda$ is a positive constant. Is there a relation between the ground state energy of $H$ and $\lambda$ i.e. is ...
user3678252's user avatar
2 votes
1 answer
169 views

Ground state interparticle distance in a system of interacting particles under harmonic confinement

Let us consider a system of two particles interacting via Coulomb force and being acted upon by a global harmonic oscillator potential. So, the system Hamiltonian is, $$H=\sum_{i=1}^{2}\frac{p_i^2}{2m}...
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Does the state change, when the Hamiltonian changes?

Consider the Hamiltonian \begin{equation} H = \frac{p^{2}}{2m} + \frac{1}{2} m\omega^{2}x^{2} - \theta(t) qEx \end{equation} where $\theta(t)$ is $0$ for $t = 0$ and $1$ for $t > 0$. If at $t = ...
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What is the physical meaning of the vacuum state in the BCS ground state?

the BCS ground state is: $$|\psi_G\rangle= \prod_k(u_k+v_kc_{k,\uparrow}^+ c_{-k,\downarrow}^+)|\phi_0\rangle $$ now, i always believed that the vacuum state $|\phi_0\rangle$ was a state with no ...
Valerio Actis Dato Casale's user avatar
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Ground eigenstate of the quantum harmonic oscillator with the interacting vacuum $| \Omega \rangle$

According to this video (at the timestamp), the professor writes down the derivation of the ground state of the 1D quantum harmonic oscillator. Here is the screenshot from the slides of where she does ...
Tachyon's user avatar
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1 answer
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Ground state of Bogoliubov quasi-particles (simpler version)

This is a simplified version of one of my previous questions. Let $b_1, b_2$ be two boson operators; their vacuum is denoted as $|0\rangle$, i.e. $b_i |0\rangle = 0$. We can make a canonical ...
Zhengyuan Yue's user avatar
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2 answers
69 views

What is the quantum state of a particle sitting at rest at the minimum of its classical potential?

Suppose a particle, moving in a potential $V(x)$, is known to be at rest, at one of the local minima of its classical potential. Therefore, classically its total energy is at its local minimum. Given ...
Solidification's user avatar
1 vote
1 answer
352 views

Quantum fluctuations are not real, but yet they can create observable phenomena?

I have read these What are quantum fluctuations, really? Quantum fluctuation https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/ and found out that quantum fluctuations ...
Tachyon's user avatar
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3 votes
4 answers
242 views

Why energy-positivity?

In any relativistic quantum field theory, we require that the spectrum is bounded from below. The typical explanation is that this condition enforces the stability of the theory. However, to me this ...
Prox's user avatar
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4 votes
1 answer
339 views

Definition of the $n$-point Green's function and vacuum state in QFT

Reading different books, I've come upon two apparently different definitions of the $n$-point Green's function. For simplicity, let's consider a real scalar field $\hat{\phi}(x)$ (in the Heisenberg ...
Mr. Feynman's user avatar
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2 votes
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Does the ground state of interacting of interacting spinless/scalar bosons in a centrally symmetric potential have angular momentum 0? [duplicate]

Motivated by this question: If electrons were spinless/scalar bosons, would atomic ground state configurations necessarily have total orbital angular momentum zero?. Can we make a group-theoretical ...
Roger V.'s user avatar
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1 vote
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If electrons were spinless bosons, would atomic ground state configurations necessarily have total orbital angular momentum zero?

My motivation for this question comes from the periodic table. There, the many-body ground state electronic configurations of certain atoms like boron or carbon can have a nonzero total orbital ...
user196574's user avatar
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-2 votes
2 answers
123 views

Paradox between Heisenberg and ground state? [closed]

According to Heisenberg principle if the electron is near the nuclei it is more likely to have a greater momentum $p$. So the energy must be greater. But the electron loses energy and has in fact ...
Mercury's user avatar
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1 answer
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Finite quantum harmonic oscillator and existence of a ground state

I am having some problems with a finite, shifted quantum harmonic oscillator potential, and the theorem that states: Any attractive potential in one dimension must have at least one bound state. Let'...
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2 votes
1 answer
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How can we measure cosmological constant if we can't measure ground state energy?

From what I understand, we can only measure energy differences (see for example Peskin & Schroeder page 21, last paragraph), and therefore the ground state of a system cannot really be measured. ...
Y2H's user avatar
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0 answers
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Do different Hamiltonians result in different ground states?

I'm learning density functional theory. In the proof of Hohenberg–Kohn theorem I, we assume that different Hamiltonians result in different ground states. Is it true? In general, for example, we can ...
jiawei chen's user avatar
7 votes
2 answers
678 views

Is Hartree-Fock (HF) a ground state theory?

To calculate the orbitals in Hartree-Fock (HF) theory we imply the variations principle, so we try to find the wavefunction which minimises the energy $\left<\psi|H|\psi\right>$. This ...
Lockhart 's user avatar
1 vote
0 answers
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Beta-decay of a Tritium [closed]

Calculate the probability of a Tritium beta decay into ground state of a Helium ion with perturbation theory. What should I start with? I lack any ideas.
LevGor's user avatar
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0 answers
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Ground state of hydrogen atom, $e^{-\kappa r }$ or $e^{-\kappa r }/ r$

The ground state must be an $s$-wave state, so it depends only on the radius $r$. I cannot remember the exact form, but I know it must be one of the two. Is there any simple way to determine which one ...
poisson's user avatar
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2 votes
1 answer
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Is the average position for the ground state of a 1D simple harmonic oscillator zero? [closed]

My textbook claims the average position of the $n$-th state of 1D simple harmonic oscillator (SHO) is zero, which means $$ \def\bra #1{\langle #1 |} \def\ket #1{| #1 \rangle} \def\braket #1{\langle #1 ...
IvanaGyro's user avatar
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Excited state at room temperature and near 0 Kelvin

What does the excited state of the electron of a hydrogen atom look like at room temperature? What does the almost ground state look like slightly above 0 Kelvin?
HolgerFiedler's user avatar
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1 answer
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Ground state of electrons in an atom

When we talk about the ground state of the electrons in the atom, do we mean its state at room temperature?
HolgerFiedler's user avatar
1 vote
1 answer
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Relevance of the Jahn-Teller theorem

Jahn and Teller stated in their paper that All non-linear nuclear configurations are therefore unstable for an orbitally degenerate electronic state. Thus if we know of a polyatomic molecule that the ...
poisson's user avatar
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4 votes
1 answer
819 views

Ground state of Bogoliubov quasi-particles

Consider a set of boson/fermion creation and annihilation operators satisfying the canonical (anti-)commutation rules (CCR/CAR): $$ [a_i, a_j]_\eta = [a^\dagger_i, a^\dagger_j]_\eta = 0, \quad [a_i, ...
Zhengyuan Yue's user avatar
1 vote
1 answer
213 views

General remarks on the Hubbard model in the strong coupling limit

Some results are known for the Fermi-Hubbard model under certain assumptions. For instance, it is known that at half-filling and in the strong coupling limit, the Hubbard model reduces to a Heisenberg ...
Karim Chahine's user avatar

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