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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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Why the ground state energy of bosons are 0 at T=0K ? Does it violate Heisenberg's Uncertainity Principle at 0K?

Bosons obey Heisenberg's Uncertainity Principle but do not Pauli's Exclusion Principle. That's why in Bose Condensation we get a large amount of particles in a single state i.e. ground state at T=0K. ...
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Calculating Simple Ground State Energy Of Hydrogen From Geminal Spin Function

I'm very new to quantum stuff and I'm experimenting, but I'd like a good explanation here if you can give it. Here's the circuit diagram and the results. I'm seeing from this paper that you can get ...
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Does the ground state of the Schrödinger equation, in any number of dimensions, always have constant phase?

I just read this argument in this paper (PDF). It suggests that, from variational principles, you can show that you can always lower the energy of a state by making the phase constant, thus resulting ...
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Degenerate ground state of Hamiltonian from analytical perspective

Suppose I have a Hamiltonian that depends on the continuous vector parameter $\boldsymbol{\theta}$, and the ground state corresponds to line/plane or some other $1$ to $p-1$ dimensional subspace of ...
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In the Schrödinger picture, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\phi\rangle=\phi(\mathbf x)|\phi\... 0answers 22 views Finding mathematically the ground state density in DFT I've posted this question in the chemistry exchange, but it did not get any answer; maybe it is better suited here? To find the ground state density in DFT, you set the following Lagrangian: $$L = E[... 0answers 60 views Showing in the classical limit an operator U = \langle \Omega | U |\Omega \rangle Let \Omega be the ground state of the Hilbert space \mathcal H. How can I show that in the classical limit, an operator U goes to \langle \Omega | U |\Omega \rangle? Attempt. This is ... 1answer 36 views Cosmic strings and ground state degeneracy in SSB There are two conflicting perceptions that I have regarding the notion of ground state post-SSB. Consider the Higgs mechanism e.g. for the electroweak theory. On the one hand, we say that the vacuum ... 1answer 64 views The “Hartree-Fock energy” in the Feynman formalism vs the Hartree-Fock method This question has been previously asked, but I do not understand the answer. When calculating the ground state energy of an interacting system by a perturbative expansion in terms of Feynman diagrams,... 2answers 110 views How to actually find a Hartree-Fock ground state? I am interested in finding the Hartree-Fock ground state for a system of interacting fermions (with totally local scattering, so a delta-function interaction potential). I have read through some ... 1answer 115 views What's the ground state wave-functional of a fermion? The vacuum state, free field wave-functional of a scalar field \hat\phi(x) in the Schrödinger representation of quantum field theory is$$\begin{array}{cl} \Psi_0[\phi] &= C\prod_k e^{-\omega(k)... 1answer 38 views In the ground state properties of electron gas, is$V$the volume of all the metal or the volume of a cell of the lattice? In the ground state properties of electron gas (Sommerfeld theory), is$V$the volume of all the metal or the volume of a cell of the lattice? I thought the latter because the Born—von Karman boundary ... 0answers 38 views Why are degenerate ground states interesting? Studying the Su-Schrieffer-Heeger chain I have learned that the model has two different phases, one which is called topological and the other one trivial. In the notes it says that these phases are ... 2answers 32 views Hamiltonian and Supercharges Mirror Symmetry p.188 Eq. 10.109 states that $$H \left\vert \alpha\right> = 0 \Longleftrightarrow Q \left\vert\alpha\right> = \overline{Q} \left\vert\alpha\right> =0. \tag{10.109}$$ I dont ... 2answers 39 views Energy level below ground state Can an electron occupy an energy level lower than its ground state? Do electrons come closer to each other at 0K temperature? 1answer 65 views SUSY Breaking in the Vacuum Under what conditions is supersymmetry preserved in the vacuum state? In particular, suppose I have some super potential$W(x)$which does not permit normalizable ground-state wave functions (such as$...
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The second is defined as the duration of 9,192,631,770 cycles of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. So what is ...
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Question about fundamental states on an finite well

My question is the following, when we search for the bound states a finite well potential we have solutions symmetric and antisymmetric so we get two families of solutions. In this case, the ...
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Why does a system assume ground state at absolute zero temperature?

I am going through Huang, Statistical Mechanics. He says at 0 kelvin, a quantum system assumes ground state so that $S=k_B ln(G)$ holds where $G$ is the degeneracy of the ground state . My question ...
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What happens to a particle in a well if the well is made bigger? [duplicate]

Let's say we have a particle in an infinite well, and let's also say it is in the ground state. Now we make the well bigger by very quickly moving one of the boundaries of the well. How do we ...
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Topological materials and fractionalized excitations

I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
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Whether to add the chemical potential in the 2nd quantized Hamiltonian (Piers Coleman)

I am reading the Piers Coleman's book : Introduction to Many-body Physics. And I am now struggling with the construction of the 2nd quantized Hamiltonian. Typically I don't know whether to add the ...
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2 Particles in a Landau level interacting via a Central Potential

I am studying Robert Laughlin's paper about the Franctional Quantum Hall Effect http://gtwlx.jpkc.fudan.edu.cn/reference/FQHE-T.pdf . In it, while he is setting up his motivation for the Laughlin ...
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Ground state degeneracy [closed]

Today, I have learned from Prof. Cramer's (univ. of minnesota) lecture that the ground state can have degeneracy. and he showed entropy $S = k_{b} ~ ln_{}~ \bf{n}$ , if ground state is $\bf{n}$ - ...
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Problem with interaction ground state in Peskin and Schroeder (Chapter 4)

In Peskin and Schroeder Section 4.2, in the process of deriving the form of the interacting ground state, the authors seem to add an extra factor $e^{iH_0(T+t_0)}$ in the second line of eq 4.28 (...
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Is ground state and vacuum state the same thing?

Vacuum state is the lowest possible quantum energy state but isn't this also the definition of the ground state?
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Energy of an electron in triangle potential [duplicate]

I'm trying to get the fundamental state of an electron in a potential, as in: $$V(X)=e|x|$$ Where $e$ is a constant. To start with I want to solve it with $e=1$, then where $e$ is big enough that it ...
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ground state of spin chain with $Z_i X_{i+1} Z_{i+2}$ interaction

the problem comes from transverse field Ising model, with an extra 3-spin interaction term H=H_0+H_1+H_2=-h\sum_{i=1}^{N}X_i -\lambda_1 \sum_{i=1}^{N-1}Z_i Z_{i+1}-\lambda_2 \sum_{i=1}^{N-2}Z_i X_{i+...
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Why is the ground state energy of particle in a box not zero?

I understand that we want to solve for non-zero values of wave function. I always thought that is to avoid the obvious answer to Schrodinger equation. But from physical standpoint, if we have a ...
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For the ground state of tin, why is it not possible to have a triplet D state?

I have been looking at electron configuration and understand the use of hund's rules, the Aufbau principle and the Pauli exclusion principle but am having difficulty with a question that has come up ...
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Grounds state of carbon - Hunds Rule

I have a question about Hund's second rule for the ground state of carbon. Why is it that when S=1, L has to be 1 instead of 2? I don't get the whole symmetric/ antisymmetric argument. Why is L=2 ...