# What is many-body bound state?

Bound state by definition is a state when particles are bounded together, so then "many-body bound state" would be bound state for a system of many bodies. Then I have several puzzles:

1. is the state when many particles are confined in a box or some traps could be viewed as many-body bound state?
But usually bound state is due to interactions between themselves not to external potentials. So is it just a favor of definition, so then trivial?

2. is solid/liquid state a many-body bound state?
I am just wondering why few people would say that. The problem may be that: here a solid/liquid state is actually a phase, not a single quantum state. So then is a solid/liquid at zero temperature, meaning that it is in a single quantum state, could be viewed as a many-body bound state?

edit 17/11/2014
Thanks to @ACuriousMind, I find that my "definition" of bound state seems to be a circular-type. I just refer to its literal meaning. To be accurate, say by wiki:
In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space. The potential may be either an external potential, or may be the result of the presence of another particle.

If the external potential could be included, then particles in a box or in a trap could also be viewed as in bound state. Any reason to object?

• bound states can also apply to single particles, bound states means that they are in a sense states with bounded energy or orbit (in various contexts). Bound states in quantum mechanics as a concept is used from the classical analog – Nikos M. Nov 15 '14 at 22:17
• @Nikos M. Agree. But any more information concerning my puzzles? – Mathieu Nov 16 '14 at 7:13
• "Bound state by definition is a state when particles are bounded together" - Circular definition is circular. – ACuriousMind Nov 16 '14 at 15:08
• Can I use Chinese here？ – Wang Yun Mar 7 '16 at 11:14

If the external potential could be included, then particles in a box or in a trap could also be viewed as in bound state. Any reason to object?

In the quantum mechanical framework particles in a box or particles in a trap can only have meaning if the term "particle" is elementary, or a complex of elementary particles, as atoms and molecules are.

In this framework already the atoms are composites of elementary particles that may be described collectively with quantum mechanical models .

The electrons around the atoms are described by a shell model .

The nuclei of the atoms are described by a shell model :

the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator.

The square well potential is the "particle in the box" one.

So yes, many body bound states exist and are described by quantum mechanical models.

As dimensions grow larger crystals are a many body bound state macroscopic manifestation. They are not in a box, but are arranged geometrically depending on the attractive and repulsive forces in the lattice.