Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

2
votes
1answer
60 views

Choosing approximate eigenfunctions

In the variational approach of estimating the ground state energy of a system we choose an approximate eigenfunction dependent on certain parameters and then minimize the expectation value of the ...
0
votes
1answer
76 views

Schrodinger's Equation in three dimensions

Consider Schrödinger's Equation, $$H=\sum^3_{i=1} \frac{p^2_i}{2m_i}+V(x_1,x_2,x_3).$$ In one dimensional case, we can analyse the shape of the potential, i.e $$V(x)=\frac{1}{2}m_1 \omega^2_1 x^2$$ ...
0
votes
1answer
47 views

Spin-1 Heisenberg model, the AKLT model, and their ground states

I am reading literature on quantum spin chains and matrix product states, and I notice similar arguments regarding the spin-1 antiferromagnetic Heisenberg model, $H_{H} = \sum_i S_i \cdot S_{i+1}$, ...
1
vote
1answer
83 views

Accuracy of Heisenberg Uncertainty Principle for estimating ground state energy of particle in potential well

I've understood the assumptions and logic behind the 'proof' that the ground state of a particle in an infinite potential well has a non-zero energy using the Heisenberg Uncertainty Principle. ...
2
votes
0answers
86 views

$k$-local Hamiltonian with long range entangled ground states?

Is it possible, and if yes, is there a relatively simple example of a Hamiltonian that only has k-local terms but its ground state always has entanglement beyond $k$ sites? For instance if $H = H_{...
2
votes
2answers
316 views

What is ground state useful for?

Many textbooks and research are oriented to computing or finding the ground state of a quantum mechanical system. Why is it such a big deal? What can be done once one has the ground state?
3
votes
3answers
419 views

What is the “lowest energy”?

In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? ...
3
votes
0answers
46 views

Physical meaning that an energy functional has no minimizer

It is well known that the Hamiltonian of a system might not have a minimizer, even the Hamiltonian is bounded below. For example, let us consider the cubic time independent Schrödinger equation \begin{...
1
vote
1answer
41 views

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 ...
0
votes
1answer
59 views

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 ...
0
votes
1answer
45 views

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 ...
5
votes
1answer
72 views

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 ...
2
votes
1answer
96 views

How does the normalization of an $n$-particle state $|n_{\mathbf{k}}\rangle$ work?

You can expand the free, real scalar field in the following manner $$ \phi(x) = \int \frac{d^{3}\mathbf{k}}{(2\pi)^3} \frac{1}{\sqrt{2\omega_{\mathbf{k}}}} \bigg[ e^{- i \omega_{\mathbf{k}}x^0+i \...
0
votes
0answers
84 views

Triplet states and the Hund's rule in identifying the ground state configuration (open shell)

I referred to some of the questions about Hund's rule on StackExchange, such as this for example, but still wasn't able to have my question resolved. (the wikiepdia page has $E_{ex} = C - \frac{1}{2}...
1
vote
0answers
39 views

Supposing that a quantum system is in a degenerate ground-state, is it valid to call this a “superposition” of the possible groundstates?

According to the adiabatic theorem, a quantum system can be prepared in the ground-state of some Hamiltonian $H_f$ if it starts in the ground state of some Hamiltonian $H_I$ and is varied "slowly" ...
0
votes
1answer
66 views

Simple iterative method to obtain any ground state given Hamiltonian operator

So, I'm considering the operator $\frac{h_0}{\bf H}$ with $\bf H$ any hamiltonian operator and $h_0$ a small non-zero positive constant with dimensions of energy and assumed to bound by below all ...
0
votes
1answer
47 views

How can I differentiate ground state and excited state hadrons?

How can I differentiate ground state and excited state hadrons ? What is the difference between their quantum numbers?
2
votes
1answer
144 views

Lagrangian multiplier and ground state search

I'm trying to understand the paper of Schollwoeck. On page 64, equation 203 he states: In order to solve this problem, we introduce a Lagrangian multiplier λ, and extremize $$ \langle \psi | ...
1
vote
0answers
58 views

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 ...
4
votes
1answer
196 views

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 ...
1
vote
1answer
919 views

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} $ - ...
3
votes
1answer
152 views

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 (...
10
votes
3answers
1k views

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?
-2
votes
2answers
210 views

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 ...
0
votes
1answer
107 views

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+...
7
votes
3answers
7k views

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 ...
1
vote
1answer
81 views

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 ...
1
vote
1answer
189 views

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 ...
2
votes
1answer
64 views

Renormalization group to predict the ground state of a Hamiltonian

It is slightly difficult to phrase my question because I'm looking more of an entry point to something I know is a large field rather than a solution to a specific problem. I occasionally see papers ...
0
votes
0answers
34 views

What phase of an electromagnetic wave is the ground state?

I have read that the uncertainty principle applies to electromagnetic radiation, and the ground state could not be sitting on the lowest energy point, because then it would have definite position and ...
2
votes
1answer
617 views

Position probability distribution of a particle in an infinite square well: classical versus quantum

The wave-function for a single particle in a potential well of width $L$ is given by the relation $$\Psi_n(x)=\sqrt{\frac 2L} \sin(K_n x)$$ where $K_n$ is $(n+1)\pi/L$ and $n$ is a positive integer. ...
0
votes
1answer
87 views

Ground state of electrons in diatomic molecule and probability to find electron near a shell at the ground state

Question: The effective Hamiltonian of an outer-shell electron in a diatomic molecule is given by $$H = \left(\begin{array}{cc} E_1 & t \\ t & E_2 \\ \end{array} \right)$$ where $E_1$ ...
0
votes
0answers
248 views

How to get ground state wave function in path integral method?

For a fermion field with the nearest interaction on a square lattice. How once could determine ground state field or ground state wave function in path integrals? In general how one can determine wave ...
1
vote
1answer
289 views

Using the Heisenberg Uncertainty Relation to Estimate Ground State Energies

In Shankar's Principles of Quantum Mechanics, he applies the HUP to estimate the ground state energy of the Hydrogen atom. In the proof, it is said that the first step to minimizing the expectation ...
12
votes
1answer
354 views

Explicit nontrivial examples in quantum mechanics: ground state degeneracy

Ground state degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and commutes with the Hamiltonian of the system. I just want to find a potential $V(\...
2
votes
2answers
1k views

Finding the ground state of a Hamiltonian Matrix

I have numerically constructed a Hamiltonian matrix. I am currently finding the ground state by full diagonalisation of the matrix (with the GSL library) and finding the most negative eigenvalue and ...
1
vote
1answer
84 views

What's the relation between zero temperature and ground state of interacting many body system?

In the famous monograph "Many body physics" by Mahan there is a statement about the corresponding relation between the zero temperature and the ground state: "Furthermore,the zero temperature ...
1
vote
0answers
146 views

Ground state of QFT with $\varphi^4$ interaction

What is the ground state (Vacuum state) of a scalar field with a $\varphi^4$ interaction? Can we analytically write an expression for it?
4
votes
5answers
1k views

If an electron is in ground state, why can't it lose any more energy?

As far as I know, an electron can't go below what is known as the ground state, which has an energy of -13.6 eV, but why can't it lose any more energy? is there a deeper explanation or is this ...
-1
votes
1answer
720 views

Why is $\langle x \rangle =0$ for the ground state hydrogen atom?

From Griffiths, Introduction to Quantum Mechanics, 2nd ed: I found $\langle r \rangle =\frac{3a}{2}$ and $\langle r^2 \rangle =3a^2$. Now I need to find the expectation value of x. However, I don't ...
1
vote
1answer
116 views

Finding an approximate expectation value $\langle E_0|\hat{O}|E_0\rangle$ when i dont know the ground state?

I'm assuming that i know the hamiltonian although i don't know it's ground state $|E_0\rangle$ and that i have a way to find $|\psi(s)\rangle\equiv e^{-\hat{H}s}|{\psi}\rangle$, $\forall s\in\mathbb{R}...
1
vote
1answer
104 views

Ground state(s) of electron and dependence from temperature and gravitational potential

Reading this question What happens to an electron in a molecule once it has absorbed a photon and transitioned? it occurs the question to me is the ground state say of a hydrogen electron the only one?...
4
votes
0answers
376 views

The ground state of arbitrary Potential Function

How can one say that the number of nodes in the ground state must be nodeless . And how one can ensure that, when one gets up in the energy spectrum, for consecutive States the difference of number of ...
-4
votes
2answers
1k views

When quantum physics say an electron has angular momentum 0, does it mean it stopped?

When at some quantum state, it is said about an electron that its momentum is zero, does it mean it has no mass? Or no scalar speed? How can an electron have zero momentum? Does it "condensates" like ...
15
votes
4answers
1k views

Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function?

Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the ...
0
votes
1answer
54 views

Ground state metric?

In kaluza-klein theory, there's a notion of a "ground state metric" after compactification. What is the meaning of the term "ground state metric"?
-2
votes
1answer
613 views

Ground state energy of spin 1 particle

So I have this Hamiltonian for a particle with spin 1: $$ H=aS_{z}^2+\frac{\hbar\omega}{\sqrt2}S_{x}$$ where ($a$ and $\omega$ both real constants): $$ S_{z}=\hbar\begin{pmatrix} 1 & 0 & 0 \...
16
votes
2answers
260 views

What's the lowest nuclear charge $Z < 1$ that will support a bound two-electron ion $(Z,2e^-)$?

In my programming project I calculate the minimal energy of an atom with 2 electrons in the $L=0, S=0$ state, using a Hylleraas wave function. The values I find for $Z=2$ (He) and $Z=1$ (H$^-$) are ...
1
vote
1answer
40 views

Isn't there any analog between angular momenta in Classical/Quantum Mechanics, especially for the ground state?

By the ground state, I mean something like the state of the hydrogen atom with the lowest its total energy, where the quantum number $l$ is 0, which means we can't get any orbital angular momentum at ...
0
votes
2answers
86 views

Lowest energy product state of a local hamiltonian

Lets consider one-dimensional spin chain with periodic boundary condition and $N$ sites. We are given a translationally-invariant local hamiltonian $H$ which is defined as $H=\sum_{i=1}^N h_{i,i+1}$, ...