# 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.

197 questions
Filter by
Sorted by
Tagged with
37 views

### Absolute zero and zero-point energy

What will be the theoretical temperature of ideal solid state matter where all the atoms have only zero-point quantum fluctuation? Is it exactly 0.00000 K or still some 0.000000x K?
• 679
90 views

387 views

104 views

### Time free evolution of the harmonic ground state (Quantum mechanics)

I have an atom in the ground state for a harmonic potential. At time $t = 0$ the parabolic potential is switched off. How can I derive the time evolution of the wave function $\psi(t; x)$ during the ...
• 23
55 views

### Ground state in $k$-space convert back to real space - spinless non-interacting fermionic system

Say, you have the following spinless non-interacting fermionic (1D) Hamiltonian: $$\hat H = -t \displaystyle \sum_{\langle i,j\rangle} (\hat c_i^+ \hat c_j + \hat c_j^+ \hat c_i)$$ Diagonalizing it (...
• 63
1 vote
62 views

### Existence of Ground State of Dirac equation

In chapter four of Ryder, the author showed that there exists a ground state $|0\rangle$ for the Kelin-Gordon equation, just like the case of the linear harmonic oscillator. However, I was not able to ...
• 1,355
1 vote
69 views

### Exciton state, ground state and completeness relation

Considering the exciton eigensystem $\mathcal{H} | \lambda \rangle = E_\lambda |\lambda\rangle$ with the Hermitian Hamiltonian $\mathcal{H}$ and wave function $|\lambda\rangle$. I'm thinking about the ...
56 views

### Energy values in case of 1D infinite potential well

As it is depicted in the picture, there are 4 types of potential wells and if $E_1, E_2, E_3, E_4$ represent the ground state energies of the particle confined in those wells, what should be the ...
• 153
91 views

### Exact ground state energy of the noninteracting one-dimensional Bose Hubbard model? [closed]

The Hamiltonian of Bose-Hubbard model reads as $$H = -J\sum_{<i,j>}a_i^\dagger a_j + h.c. + \frac{U}{2}\sum_i n_i(n_i - 1)$$ In the non-interacting case where $U=0$, what is the ground state ...
59 views

### Exact eigenfunctions of two interacting identical particles [closed]

While I was reading about quantum states of $N$ interacting identical particles, I realized that I don't understand some fundamental things. So In order to clear my confusion, I decided to consider a ...
• 407
47 views

### What is the ground state of the Hubbard model for $t = 0$?

I am new to the Hubbard model and it is not clear to me how we go to the so called 'atomic limit' where $t = 0$. So we only have a $U > 0$ term in the Hamiltonian. This should be a trivial problem ...
• 145
1 vote
52 views

### Tensor Networks with Julia and implementing given Hamiltonian

I have this Hamiltonian: (ref: https://arxiv.org/abs/1302.5843) I want to solve this Hamiltonian by using tensor networks. I wanted to make the implementation with ITensors, Julia. However, I am ...
• 11
81 views

### Ground State calculation for defined 2D Ising Model with tensor networks

I have a Hamiltonian and 2D spin-lattice system. I am trying to find a ground state configuration. Spin interactions are long-ranged so I am trying to use PEPS to approximate. My question is this: ...
• 11
1 vote
46 views

### WKB approximation problem [closed]

I have some issues on solving this problem: use the WKB method to estimate the ground state energy of a particle of mass $m$ that moves in a three dimensional potential $V(r)=kr$, where $k$ is a ...
• 11
1 vote
42 views

### Vacuum manifold and fermion condensation

Vacuum manifold is just another name for the manifold spanned by the ground states of quantum field theory. It is also called moduli space. According to https://en.wikipedia.org/wiki/Vacuum_manifold, ...
• 3,888
331 views

### Is the zero point energy of this system zero?

Consider the following Hamiltonian: $$\hat H=\frac{\hbar\omega}{2}(\hat x^2+\hat p^2)-\frac{\hbar\omega}{2}\hat 1 =\frac{\hbar\omega}{2}(\hat x^2+\hat p^2-\hat 1 )$$ After defining annihilation and ...
• 1,273
27 views

### Minimum energy eigenvalue [duplicate]

Why is the energy eigenvalue is always greater than minimum potential for a particle moving in a certain potential?
41 views

### How to calculate the ground state of bosonic hamiltonian?

I am trying to find the ground state of the Hamiltonian: $H=\sum^N_{K=i}\omega_kb_k^\dagger b_k$ where $b_k=\frac{1}{\sqrt{N}}\sum^N_{N=i}\exp(\frac{2\pi ikn}{N})b_n$. Any hints on how to proceed?
• 1
42 views

### Boson Einstein condensation of free particles

Under Schrödinger's representation, for free particles without spin, each eigenstate vector is $\delta(x-x_0)$, corresponding to the eigenvalue $x_0$, each position in the 3-dimensional configuration ...
• 575
34 views

### Elements Below Ground Energy State

I have been hearing things about people getting elements like hydrogen below the ground energy state. I don't understand how that is even possible. The more interesting thing is how this actually ...
318 views

### Do the Gell-Mann and Low Theorem and Haag's Theorem contradict one another?

I was wondering if these two theorems do not conflict with one another in some sense. It sees as if one allow us to move from the free to the interacting theory, while the other forbids it.
• 569
1 vote
72 views

### What type of regulation is being employed?

As already mentioned in this post. In the context of QFT, the kernel of integration for the overlap of a field configuration ket, $| \Phi \rangle$ with the vacuum $|0\rangle$ in a free theory is given ...
• 4,070
151 views

• 357
31 views

• 245
160 views

### How to determine the ground state of quantum harmonic oscillator like Hamiltonian?

For the time-dependent Hamiltonian $$H = \frac{\hat{P}^2}{2m} + \frac{1}{2} m\omega^2\hat{X}^2 + m\omega^2vt\hat{X} +v\hat{P}$$ I would like to calculate the ground state, more precise, the stationary ...
• 407
1k views

### Why is the ground state important in condensed matter physics?

This might be a very trivial question, but in condensed matter or many body physics, often one is dealing with some Hamiltonian and main goal is to find, or describe the physics of, the ground state ...
• 4,366
1 vote