# What is Ground state: Definition and 275 Discussions

The ground state of a quantum-mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum.
If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system.
According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature.

View More On Wikipedia.org
1. ### Fourier transform of t-V model for t=0 case

To compute the Fourier transform of the ##t-V## model for the case where ##t = 0##, we start by expressing the Hamiltonian in momentum space. Given that the hopping term ##t## vanishes, we only need to consider the potential term: $$\hat{H} = V \sum_{\langle i, j \rangle} \hat{n}_i \hat{n}_j$$...
2. ### I Instability of hydrogen ground state if the time-reversal operator is unitary

Apparently if we try to represent the time reversal operator by a unitary operator ##T## satisfying ##U(t)T = TU(-t)##, then the ground state of hydrogen (the hamiltonian of which is time-reversal invariant) is unstable. But if ##T## is anti-unitary (i.e. ##\langle a | T^{\dagger} T | b \rangle...
3. ### Using Variational Principle to solve ground state energy

First I picked an arbitrary state ##|ϕ⟩=C_1|φ_1⟩+C_2|φ_2⟩+C_3|φ_3⟩## and went to use equation 1. Realizing my answer was a mess of constants and not getting me closer to a ground state energy, I abandoned that approach and went with equation two. I proceeded to calculate the following matrix...

42. ### Ground state of 3 noninteracting Fermions in an infinite well

In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...
43. ### I Exploring the Ground State Lamb Shift: Advances and Controversies

What exactly is the so-called "Ground State Lamb Shift". It seems to have been an 'in vogue' quantity up till 1995 or so - then vanished from the literature ?? It's the 'self energy' or something like that of an electron in H 1S orbital. A scientist (at NIST) told me it's a term that has gone...
44. ### I Ground State Energy of a Potential: λ2px2/2m+0.5kx2

I am having a doubt that if Id lho potential is Given of the form λ2px2/2m+.5kx2 then whether the ground state energy of the system is λ2/4ħω+1/4ħω
45. D

### I 2D LHO calculate ground state energy

A question I have faced in exam to calculate ground state energy Given Hamiltonian 1/2m(px2+py2)+1/4mw2(5x^2+5y^2+6xy) ground state energy has to be obtained Its clear that the Hamiltonian is a 2D LHO Hamiltonian but what for the term 3/4(x+y)2
46. S

### A Is there an alternative form of the zero point energy?

Hi, is there an alternative form of the zero point energy for free electrons, where there is no space interval L to be quantized in? The zero point energy for electrons in an atom can be simplified to a variant where Z^2 is present in the nominator, however, these are not free electrons. Can a...
47. ### Expectation value of mean momentum from ground state energy

1. The problem statement Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2} Knowing that the ground state of the particle at a certain instant is described by the wave...
48. ### I Why drop the vibrational ground state energy

This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...
49. ### A Several ground state calculations at once

Suppose I want to find the ground states corresponding to several Hamiltonian operators ##\left\{ \hat{H}_i \right\}##, which are similar to each other. As an example, let's take the ##\hat{H}_i##:s to be anharmonic oscillator Hamiltonians, written in nondimensional form (##\hbar = m = 1##) as...
50. ### B How do electrons behave when energy is added to an atom's ground state?

Yah electrons existing the lowest possible energy state! Now suppose, we throw a beam of light towards a ground state of a atom. I heard/know electrons will take up energy from the photon "hv", and go to the next energy level i.e. excited state. Now my point is, is it only the valance electron...